Frontiers of Assembly and Manufacturing: Selected papers from ISAM'09'

Frontiers of Assembly and Manufacturing Sukhan Lee, Raúl Suárez, and Byung-Wook Choi Frontiers of Assembly and Manuf...

Author: Sukhan Lee | Raúl Suárez | Byung Wook Choi

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Frontiers of Assembly and Manufacturing

Sukhan Lee, Raúl Suárez, and Byung-Wook Choi

Frontiers of Assembly and Manufacturing Selected Papers from ISAM 2009

ABC

Prof. Sukhan Lee School of Information and Communication Sungkyunkwan University 300 Chunchun-Dong, Jangan-Ku Kyunggi-Do 440-746 Korea E-mail: [email protected] Dr. Raúl Suárez Feijóo Researcher IOC-UPC Av. Diagonal 647, planta 11 08028 Barcelona, Spain E-mail: [email protected]

ISBN 978-3-642-14115-7

Dr. Byung-Wook Choi International Affairs Center and Principal Researcher Div. of Advanced Robot Technology and Director, Korea IMS Center Korea Institute of Industrial Technology (KITECH) 1271-18, Sa-1-dong, Sangrok-gu Ansan-si 426-791 Korea Email: [email protected]

e-ISBN 978-3-642-14116-4

DOI 10.1007/978-3-642-14116-4 Library of Congress Control Number: 2010929749 c 2010 Springer-Verlag Berlin Heidelberg This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Data supplied by the authors Production & Cover Design: Scientific Publishing Services Pvt. Ltd., Chennai, India Printed on acid-free paper 987654321 springer.com

Preface

The technologies for product assembly and manufacturing evolve along with the advancement of enabling technologies such as material science, robotics, machine intelligence as well as information and communication. Furthermore, they may be subject to fundamental changes due to the shift in key product features and/or engineering requirements. The enabling technologies emerging offer new opportunities for moving up the level of automation, optimization and reliability in product assembly and manufacturing beyond what have been possible. We see assembly and manufacturing becoming more Intelligent with the perception-driven robotic autonomy, more flexible with the human-robot coupled collaboration in work cells, and more integrated in scale and complexity under the distributed and networked frameworks. On the other hand, the shift in key product features and engineering requirements dictates the new technologies and tools for assembly and manufacturing to be developed. This may be exemplified by a high complexity of micro/nano system products integrated and packaged in 3D with various heterogeneous parts, components, and interconnections, including electrical, optical, mechanical as well as fluidic means. The objective of this volume is to show how the assembly and manufacturing technologies evolve along with the advancement of enabling technologies and how the emergence of a high complexity of micro/nano system products dictate the development of new technologies and tools for their assembly and manufacturing. To this end, we have chosen 19 papers, top-rated yet relevant, out of the 76 papers accepted to present at the 8th IEEE International Symposium on Assembly and Manufacturing. The 19 papers chosen are further revised into the final manuscripts for book chapters that are organized into three parts: Part I: Fixture, Grasping and Manipulation in Assembly and Manufacturing, Part II: Micro/Macro Assembly and Disassembly, and Par III: Manufacturing System Scheduling and Control. Part I, II and III are reviewed and organized by the co-editors of this volume, Prof. Raul Suarez, Prof. Sukhan Lee and Dr. Byungwook Choi, respectively. Wishing that readers find this volume stimulating and informative … Sukhan Lee Raúl Suárez Byungwook Choi

Contents

Chapter I: Fixturing, Grasping and Manipulation in Assembly and Manufacturing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary by Ra´ ul Su´ arez

1

Dual Arm Robot Manipulator and Its Easy Teaching System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chanhun Park, Kyoungtaik Park, Dong IL Park, Jin-Ho Kyung

5

Calibration of Relative Position between Manipulator and Work by Point-to-Face Touching Method . . . . . . . . . . . . . . . . . . . . Toru Kubota, Yasumichi Aiyama

21

Cutter Accessibility Analysis of a Part with Geometric Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Masatomo Inui, Kazuhiro Maida, Yuji Hasegawa

35

Automatic Determination of Fixturing Points: Quality Analysis for Different Number of Points and Friction Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jan Rosell, Ra´ ul Su´ arez, Francesc Penalba Contact Trajectories for Regrasp Planning on Discrete Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M´ aximo A. Roa, Ra´ ul Su´ arez

53

69

Modeling of Two-Fingered Pivoting Skill Based on CPG . . . . . Yusuke Maeda, Tatsuya Ushioda

85

Chapter II: Micro/Macro Assembly and Disassembly . . . . . . . . Summary by Sukhan Lee

97

VIII

Contents

Assembly of 3D Reconfigurable Hybrid MOEMS through Microrobotic Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kanty Rabenorosoa, Sylwester Bargiel, Cédric Clécy, Philippe Lutz, Christophe Gorecki

99

Modified Assembly Systems and Processes for the Mounting of Electro-Optical Components . . . . . . . . . . . . . . . . . . . . 113 J. Franke, D. Craiovan Factory Level Logistics and Control Aspects for Flexible and Reactive Microfactory Concept . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Eeva J¨ arvenp¨ a¨ a, Riku Heikkil¨ a, Reijo Tuokko Development of Structured Light Based Bin–Picking System Using Primitive Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 Jong-Kyu Oh, KyeongKeun Baek, Daesik Kim, Sukhan Lee Airframe Dismantling Optimization for Aerospace Aluminum Valorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 Julie Latremouille-Viau, Pierre Baptiste, Christian Mascle A Monitoring Concept for Co–operative Assembly Tasks . . . . 171 Jukka Koskinen, Tapio Heikkil¨ a, Topi Pulkkinen Chapter III: Manufacturing System Scheduling and Controlling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 Summary by Byung-Wook Choi Printing Pressure Control Algorithm of Roll-to-Roll Web System for Printed Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 Kyung-Hyun Choi, Tran Trung Thanh, Yang Bong Su, Dong-Soo Kim Adding Diversity to Two Multiobjective Constructive Metaheuristics for Time and Space Assembly Line Balancing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 ´ Manuel Chica, Oscar Cord´ on, Sergio Damas, Joaqu´ın Bautista Construction and Application of a Digital Factory for Automotive Paint Shops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 Yang Ho Park, Eon Lee, Seon Hwa Jeong, Gun Yeon Kim, Sang Do Noh, Cheol-woong Hwang, Sangil Youn, Hyeonnam Kim, Hyunshik Shin Resource Efficiency in Bodywork Parts Production . . . . . . . . . . 239 Reimund Neugebauer, Andreas Sterzing

Contents

IX

Self-Tracking Order Release for Changing Bottleneck Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 Matthias H¨ usig Integrated Operational Techniques for Robotic Batch Manufacturing Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 Satoshi Hoshino, Hiroya Seki, Yuji Naka, Jun Ota A Mathematical Model for Cyclic Scheduling with Assembly Tasks and Work-In-Process Minimization . . . . . . . . . 279 Mohamed Amin Ben Amar, Hervé Camus, Ouajdi Korbaa Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293

Chapter I

Fixturing, Grasping and Manipulation in Assembly and Manufacturing Summary by Raúl Su dx > d − Δ c (1) As mentioned in the assumptions, range of Δ w and Δ e are limited and are known;

Δ wmax > Δ w > Δ wmin

(2)

Calibration of Relative Position between Manipulator and Work

25

Actual work c´

Shifted touch target

e´p c´ =

dy d

Touch tool

d

[

]

dx

e´

Fig. 3 Information obtained by point-to-face touching

Touch target for robot arm

Ideal work

Actual work ∑ t´

Robot arm

m

p t´ m

∑m

Δt

Ideal work ∑t

∑w´

pt

Δyw

Δxw

∑w

Δθw

Fig. 4 Target position and its error Δ t

Δ emax > Δ e > Δ emin

(3)

Here, as we set the relative position error of work position enough large, many other error factors such as absolute positioning error, individual product errors of arms and works, etc. can be merged. But, practically, if the distance between the operation target position and touching position is very far, the modeling error becomes large. So these two should be located nearby. Adding the initial condition inequalities (2) and (3), each touching operation brings one additional inequality (1). By these additional inequalities, the range of Δ w and Δ e are shrunk. Next, we will show description of the range of work target position error Δ t which is the most important factor for target operation. We set translational component of Δ t as Δ tx and rotational component as Δ tθ . As shown in Fig. 4, Δ tx is the difference between the actual target position m pt and the ideal target position m pt and Δ tθ can be described with rotational matrices;

Δ tx = m pt − m pt RΔ t θ = m Rt m RtT

(4)

26

T. Kubota and Y. Aiyama

Existence range of target

´

∑t

Δt xmin

Fig. 5 Target position existence range

Δt xmax

Δt ymax Δt ymin ∑t

As shown in Fig. 5, the range of the target error is obtained as the range of each axis. Unknown parameters in equations (1) to (4) are Δ w and Δ e. With describing these equations with Δ w and Δ e, these problems can be solved by linear programming problem with setting equations (4) as the objective function and setting (1) to (3) as constraint functions. From this linear programming problem, we can easily obtain the range of target position error Δ t.

2.5 Touching Strategy If there is no repetitive errors, all error parameters are obtained by same number of touching times. But actually, according to number of times for touching and their positions, the range of target varies. If we chose reasonable touching points, the range can be shrunk as same size as the arm repetitive error. For this, touching positions should be distant. However, when the operation target position and touching positions are quite distant, modeling error may badly affect. So touching positions should be near to the target position.

3 Solusion with Linear Programmign Problem In this section, to write down the calibration method to a linear programming problem as shown in subsection 2.4, we rewrite the constraints functions (1) to (3) and the objective functions (4) with Δ w and Δ e.

3.1 Constraint Functions Here, we rewrite the constraint function (1) with Δ w and Δ e. From Fig. 2, since −1 −1 −1 Te = Tw Tc , TΔ−1 e Te Tw TΔ w Tc becomes TΔ e Tc TΔ w Tc . So, e e

−1 pˆc = TΔ−1 e Tc TΔ w Tc pˆ0

(5)

pc = RTc (RΔ w − I)pc + RTc pΔ w − pΔ e

(6)


p0 = [0 0 0]T ,

T pˆx = pTx 1 ,

27

Tx =

Rx p x 0 1

By first order approximation of equation (6), we obtain ⎤ ⎡ Δ ex e pc = − I RTc − RTc [pc ×] ⎣ Δ wx ⎦ Δ wθ ⎤ ⎡ 0 − xz xy 0 − xx ⎦ [x×] = ⎣ xz − xy xx 0

(7)

as a constraint function by one time touching. Here, Δ wx and Δ wθ are translational component of Δ w and rotational component respectively. By considering touching approach direction as x direction, x component of equation (7) means dx in equation (1). Then we obtain one linear constraint function for Δ w and Δ e. As repeating touching, the range of the unknown parameters Δ w and Δ e can be shrunk.

3.2 Objective Functions As same as the last subsection, we rewrite equation (4) with Δ w and Δ e. Δ t can be rewritten as; Δ tˆx = m pˆt − m pˆt = Tw TΔ wTt pˆ0 − Tw Tt pˆ0

Δ tx = Rw (RΔ w − I)pt + Rw pΔ w

(8)

RΔ tθ = m Rt m RtT = Rw RΔ wRTw

(9)

By first order approximation of equations (8) and (9), we obtain Rw − Rw [pt ×] Δ wx Δt = 0 Rw Δ wθ

(10)

as the range of the operation target position error. By calculating the maximum and minimum of each component of Δ t, we can obtain the calibrated position of the operation target.

3.3 Algorithm of Calibration The flowchart of proposed calibration method with linear programming problem is as shown in Fig. 6. At first, we set the initial conditions with equations (2) and (3). With just these conditions, we can obtain the initial target position range before calibration by solving the maximum and the minimum of equation (10). Next, after the first point-to-face touching operation, we obtain one constraint equation (7) with the touching information. Adding this equation to the initial

28


Start Set initial condition 9 9

sub to: Eq.(2)

Touch get new condition(Eq.(6)) from touch point

Calculation

solve the linear programming problem Change touch point NO

Fig. 6 Flowchart of calibration in LP problem

YES

End

conditions, we solve the linear programming problem of maximum and minimum of equation (10) again with constraints (2),(3) and one (7). If this solution of the range is enough small for target operation, the calibration is complete. But if it is not, we change the touching point and repeat this process. By repeating this process, we obtain more constraint function (7). We repeat this process until the solution becomes within a permissible range.

3.4 Operation Range of Proposed Algorithm In the proposed method, we use linear programming problem to solve the range, we use first order approximation for constraint functions obtained by touching. So, when work position error Δ w and tool position error Δ e are large, the solution may have large error against the real position. Then we have verified operation range of the proposed calibration algorithm. As pointed out at above, when orientation of Δ w becomes large, the solution becomes out of range of the actual position. When we checked, the limitation is about 10[deg]. This angle is not quite small. But, in production plant, work stands are often fixed with anchor bolt. In such cases, 10[deg] is easily occurrable error. So the limitation angle should be wider.

3.5 Expansion of Operation Range The reason why good calibration result cannot be obtained is because Δ w, the parameters of constraint functions are too large. Fig. 7 shows such case. In the left figure, the position of the actual work is very distant from the ideal work. In this case, information of touching point by one touching operation is also different from the ideal position. But during repeating the touching and solving the LP problems,


Ideal touch position

Fig. 7 Modification of ideal work position

29

Actual touch position

Actual work Ideal work Before modification of ideal work position

Modified ideal work After modification of ideal work position

the position of the ideal work position is fixed. So all information is distant from the ideal value. It is one of the important reasons. So, after each trial of touching and solving LP problem, we modify the gidealh work position to the estimated position (average of the maximum and the minimum position). With this modification, measured position can be close to the ideal position. One more artifice is as shown in the right figure in Fig. 7. Not only just modification of ideal work position, the information of touching direction should be also modified. Because in this algorithm, we assume that touching direction is normal to the contact face. By simple modification of only work position, there exist contradictions about this assumption. This modification is effective because each information obtained by one touching does not deteriorate the estimation. Then modification by each trial does not deteriorate the result. With this expansion, operation range or the algorithm is improved to the limitation about 40[deg].

4 Experiments for Algorithm Evaluation 4.1 Abstract of Experiment To validate the effectiveness of the proposed calibration method, this section shows experiments for repeatability and precision. As repeatability evaluation, we have several times experiments without changing environment and conditions and check the variation of the calibration result. As precision evaluation, we have some calibration experiments, and after this, the manipulator tries to assemble a part at the target position by position control. By success ratio, we evaluate the precision. We cannot use a ruler to evaluate the calibration result because the result also consists absolute error of the arm.

4.2 Experiment Environment Experiment environment setup is as shown in Fig. 8. MOTOMAN-HP3J, a 6-d.o.f. manipulator of Yaskawa Electric Corporation is used as a robot arm. The repetitive

30


Fig. 8 Experiment environment setup

error this arm is 0.03[mm]. At the wrist, a 6-axis force/torque sensor Nitta 70M35AM50B is attached to sense a touching probe tool contacts with the target work. As a touching tool, spherical probe is attached at the side of the gripper. For repetitive evaluation, the target work for calibration is a 120[mm] × 70[mm] × 30[mm] stainless block with 6 face milling cut. For precision evaluation, with a peg-in-hole insertion experiment, the target work is 28[mm] × 34[mm] × 30[mm] stainless blocks with oilless bush as a hole. We use two types of the bush; one has a diameter of 12 (+0.016 to +0.034) [mm] and the other has a diameter of 12 (+0.060 to +0.120) [mm]. We also use two types of stainless peg; one has a diameter of 12 (-0.017 to -0.006) [mm] and the other has a diameter of 12 (-0.043 to -0.016) [mm].

4.3 Experiment for Repeatability Evaluation As for repeatability evaluation, we have several times experiments without changing environment and conditions and check the variation of the calibration result. We locate the work ideally at (x, y, z) = (390[mm], 160[mm], 50[mm]) position. The results of 5 time experiments are as shown in Table 1 which shows each calibration result of work position and tool location error Δ e. Standard deviation of work position is about 0.04 to 0.09[mm] for position and about 0.02 to 0.04[deg] for orientation. Since the repetitive error of the manipulator is 0.03[mm], then this result shows the same order dispersion. We tried several experiments with different conditions. The tendency of results is not changed according to the conditions. In point of tool location error Δ e, standard deviation is about 0.02 to 0.03[mm]. The result of calibration of tool position seems to be well. So, we verify that even if precise tool position is not known, calibration is well achieved by the proposed way. Of course, to calibrate tool position, we need more trial of touching.


31

Table 1 Result of experiment for evaluation of repeatability

ideal 1st result 2nd result 3rd result 4th result 5th result standard deviation average

X 390.00 391.57 391.47 391.54 391.52 391.50 0.04 391.52

Work position [mm / deg] Y Z Roll Pitch Yaw 160.00 50.00 0.00 0.00 0.00 165.24 51.12 0.01 -0.20 0.01 165.18 50.97 0.01 -0.31 0.05 165.25 51.15 0.03 -0.27 0.02 165.32 51.18 -0.07 -0.27 -0.01 165.25 51.02 0.00 -0.31 0.03 0.05 0.09 0.04 0.04 0.02 165.25 51.09 0.00 -0.27 0.02

Tool pos. error [mm] X Y Z 0.00 0.00 0.00 -2.01 -2.28 0.77 -1.98 -2.29 0.80 -2.02 -2.27 0.81 -2.02 -2.23 0.80 -1.94 -2.26 0.80 0.03 0.02 0.02 -1.99 -2.27 0.80

4.4 Experiment for Precision Evaluation As for precision evaluation, we tried peg-in-hole experiment with proposed calibration method. For the operation, it does not use force control. Position control is used for the operation. The manipulator has a 6-axis force/torque sensor on its wrist just to measure actual force and to stop the manipulator when the force becomes too large. If the operation is achieved, it can be said that position precision is within dimensional tolerance that is a gap between peg and hole; Case 1: Case 2: Case 3: Case 4:

0.076 to 0.163[mm] 0.066 to 0.137[mm] 0.032 to 0.077[mm] 0.022 to 0.051[mm].

Fig. 9 shows the result. These graphs show peg position for insertion and occurred force during the insertion for each case. (a) to (d) show Case 1 to Case 4 respectively.

59 57 2 55 53 0 51 -2 x-force 49 y-force -4 47 z-force peg position 45 -6 0 1 2 3 4 5 6 7 8 9 10 time[sec] 4

(a) case1 64 62 60 58 0 56 -2 x-force 54 y-force -4 52 z-force peg position 50 -6 0 1 2 3 4 5 6 7 8 9 10 time[sec]

Force[N]

4

Fig. 9 Contact force in peg-in-hole task

2

(c) case3

(b) case2 6

64 62 60 58 0 56 -2 x-force 54 y-force -4 52 z-force peg position 50 -6 0 1 2 3 4 5 6 7 8 9 10 time[sec]

Peg position[mm] Force[N]

6

Peg position[mm]

Force[N]

6

4 2

(d) case4

Peg position[mm]

59 57 2 55 53 0 51 -2 x-force 49 y-force -4 47 z-force peg position 45 -6 0 1 2 3 4 5 6 7 8 9 10 time[sec] 4

Peg position[mm] Force[N]

6

32


Table 2 Success ratio for peg-in-hole operation Case 1 5/5

Case 2 5/5

Case 3 5/5

Case 4 1/5

In these graphs, z-force is the force against insertion direction. In Case 1 and 2, the peg contacts with the bush at 53[mm] position, and in Case 3 and 4, at 58[mm]. In Case 1, 2 and 3, small force about 2[N] occurred to perpendicular direction against insertion. But it does not disturb the insertion operation. But in Case 4, the contact force becomes larger than 4[N], then we stop the manipulator. We did each Case for several times, and almost all time has similar result as Fig. 9. Especially, in Case 1 sometimes, there is no contact force. Table 2 shows success ratio of each case experiments. With these results, we consider that position precision of 0.163 to 0.076[mm] is almost achieved. It is not enough to very precise task, but for usual assembly task with a position controlled manipulator, it seems to be well calibrated.

5 Conclusion In this paper, we have proposed a new calibration method of relative position between a manipulator and a work by point-to-face touching. It does not require advance preparation such as tool calibration. It does not require skilled operator for high precision calibration. To validate this method, we did experiments of repeatability and precision evaluation. With these experiments, effectiveness of the proposed method is verified. As future work, we want to achieve enhancement of precision of the calibration. And in this time, touching positions for calibration are manually designed. The operator considers distance between each touching point and between touching point and operation target position. Theoretically calibration precision does not depend on the touching position. But actually, convergence speed to required size of the range of target position error changes according to the touching position. So we would like to propose formulation of optimal problem where manipulator should touch to calibrate the relative position. Acknowledgements. This study is the result of a cooperative research with Yaskawa Electric Corporation. This study is sponsored By NEDO as Project for Strategic Development of Advanced Robotics Elemental Technologies.

References 1. DAIHEN CORP., NACHI FUJIKOSHI CORP.: Control Method of Industrial Robot. JP2006-293826, Japanese Patent, 2006-10-26 (2006) 2. FANUC LTD.: Teaching Position Correction Apparatus. JP2007-115011, Japanese Patent, 2005-5-10 (2005)


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3. FANUC LTD.: Apparatus for Correcting Robot Program. JP2006-293826, Japanese Patent, 2006-10-26 (2006) 4. Kin-Huat, L., Low, K.H.: Industrial Robotics: Programming, Simulation and Applications. I-Tech (2007) 5. Nakamura, H.: Industrial robot Calibration Method and Its Application for Production line. Journal of Robotics Society of Japan 15(2), 178–182 (1997) (in Japanese) 6. Roth, Z., Mooring, B., Ravani, B.: An Overview of Robot Calibration. IEEE Journal of Robotics and Automation 3(5), 377–385 (1987) 7. Yamamoto, N.: Development of Off-line Teaching System. ISCIE Journal of Systems, Control and Information 42(4), 189–194 (1998)

Cutter Accessibility Analysis of a Part with Geometric Uncertainties Masatomo Inui, Kazuhiro Maida, and Yuji Hasegawa*

Abstract. In designing a holder part of a large stamping die, designers must consider not only the functional property of the part, but also its manufacturability. The holder part is usually produced by cutting and engraving table, wall, slot and pocket features into a raw cast object. The raw cast object has inevitable large shape errors. It generally has 5 to 10mm shape difference from the nominal CAD model. This shape uncertainty causes various manufacturability problems in the milling process. The most serious problem is unexpected collisions between a cutter and raw cast object. They cause possible tool breakages and become obstructions to the cutter access to some regions on features. Since such features are not properly machined, costly re-designing the holder part is necessary. In this paper, the authors propose a manufacturability analysis system which can detect such unmachinable features caused by the shape uncertainty of the raw cast object. Proposed system computes a geometric model of a holder part with the maximum shape error by modifying the CAD model. Inverted offsetting and cutting simulations are successively applied to the model to extract the un-machinable region on the features. A system is implemented and some computational experiments are performed.

Masatomo Inui Department of Intelligent Systems Engineering, Ibaraki University, 4-12-1 Nakanarusawa, Hitachi, Ibaraki 316-8511, Japan e-mail: [email protected]

*

Kazuhiro Maida Body Production Engineering Department, Mazda Motor Corporation, 3-1 Shinchi, Fuchu, Hiroshima 730-8670, Japan Yuji Hasegawa Department of Systems Engineering, Graduate School of Ibaraki University, 4-12-1 Nakanarusawa, Hitachi, Ibaraki 316-8511, Japan

36

M. Inui, K. Maida, and Y. Hasegawa

1 Introduction To follow frequently changing customer preferences and to quickly distribute cars with high market competitiveness, automobile manufactures make efforts to shorten the production preparation time as much as possible. In the automobile production preparation process, making of stamping dies for large body parts is a very time consuming task. Curved shape part of a stamping die is usually fixed on a holder part. For precisely and stably positioning the curved shape part, hundreds of form features such as tables, walls, slots and pockets are defined on a holder. In figure 1, a holder part for a large side frame stamping die is shown. In this figure, table features are illustrated in white color. The holder part is usually fabricated by cutting and engraving the features into a raw cast object with a vertical cutter. Dark blue surface regions in figure 1 represent the un-machined surface of the raw cast object.

Fig. 1 Table features on a holder part of a large side frame stamping die

The raw cast object is produced by using “lost model casting” method. As a preparation, a model of the object is manually made by cutting, shaping and pasting some blocks of foamed styrene. The model is then buried in the casting sand and the melted metal is poured into the sand. The foamed styrene model is vaporized and its shape is replaced into the metal object. Since the foamed styrene model is soft and fragile, and it is manually made, the raw cast object of the holder part generally has 5 to 10mm shape errors from its nominal CAD model. In designing a holder part, designers must consider not only the functional property of the holder, but also its shape errors and their effects on the manufacturability.

Cutter Accessibility Analysis of a Part with Geometric Uncertainties

37

Fig. 2 An example of un-machinable features caused by some shape errors in casting. (a) CAD model of features, and (b) configuration of features with possible maximum shape error and a flat end cutter.

Since designers are not experts of machining methods, they often fail the manufacturability evaluation and design a holder part with some un-machinable form features. An example of typical un-machinable form features is shown in figure 2. White color shape shown in figure 2(a) represents a circular table feature and a rectangular table feature being adjacent to a vertical wall feature. The circular feature locates above the rectangular feature. These features are fabricated by engraving the raw cast object with a vertical flat end cutter. As shown in figure 2 (b), a specified flat end cutter can machine the rectangular feature without colliding the circular feature if they have nominal shape. In the actual machining process, the cutter may collide with the circular feature if it has possible maximum shape error, and some part of the rectangular feature may remain un-machined (see green area in the figure). In the current practice, these un-machinable features are usually detected in a later machining preparation stage. They are then reported to the designer and are resolved by re-designing the holder part. In a large and complex holder part, number of possible un-machinable features often becomes more than 50. Cost and time loss for re-designing a new holder part is a serious problem in many automobile manufactures. In this paper, the authors propose a manufacturability analysis system which can automatically detect such un-machinable features caused by the shape error. Proposed system computes a geometric model of a holder part with the maximum shape error by modifying a nominal CAD model of the part. Inverted offsetting and cutting simulations are successively applied to the model to extract the unmachinable region on the features. By using this system, holder part designers with less machining knowledge can detect such features with manufacturability

38


problems in early designing stage. The analysis result is displayed in a few minutes, so designers can modify the holder shape in a short time period. A system is implemented and some computational experiments are performed.

2 Prior Studies Many Computer-Aided Manufacturing (CAM) programs provide some functions for detecting un-machinable regions on the workpiece based on the CAD data and the milling cutter specification (for example, [6]), but they do not evaluate the effect of the shape error of the raw cast object. The manufacturability evaluation of the mechanical part was actively studied in 1990s [3]. An application of the knowledge engineering method [11], some scoring methods of the machining easiness of features based on the template knowledge [2], evaluation of the machining cost based on the removal volume of the workpiece and cutter path length [4,5], and a manufacturability evaluation method based on an assemblability evaluation technology [8] are known. These methods analyze the manufacturability of a part by applying some rules or procedures about the machining process to a nominal geometric model of the part. Since these methods do not evaluate the effect of the shape error of the raw cast object, they are not applicable to our cutter accessibility analysis problem.

3 Algorithm Outline 3.1 Input and Output Our analysis system requires a CAD model of a holder part with form feature definitions and the milling cutter specification as input data. After the computation, the system displays detected un-machibnable regions on the CAD model. The detail description of the input data is as follows; (1) A CAD model of a holder part with form features: This model represents the nominal shape (without casting errors) of a holder part to manufacture. In the model, some specifications of form features such as tables and walls are defined. Definitions of the features are given later. The authors assume that the model shape is represented as a set of triangular polygons. Most CAD systems provide a function to output the model data as a group of polygons, for example in the STL format. (2) Milling cutter specification: A milling cutter usually has 3 components, which are cutting edge, shank, and cutter holder. In our study, ball end cutter, flat end cutter and radius end cutter are assumed as cutting edge shape. Most automobile companies standardize the cutters for the holder machining. They are usually listed in an electric catalogue style, so even a designer without the expert knowledge of the milling operation can select the most preferable cutter for machining the holder part.


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Fig. 3 Form features considered in our manufacturability analysis system. They are represented with a set of triangular polygons.

3.2 Feature Definitions In our study, 7 types of form features are considered as shown in figure 3. These features are represented as a group of mutually connecting triangular polygons. They are selected based on interviews to several automobile companies in Japan; 1. 2. 3. 4. 5. 6. 7.

Table: Horizontal planar surface (see figure 3 (a)). Wall: Vertical surface. Usually it has flat shape or cylindrical shape (b). Slope: Planar surface except table and wall features (c). Pocket: Horizontal planar region completely or partly surrounded by wall features (d). Slot: Special pocket feature having two mutually parallel adjacent wall features (e). Hole: Vertical holes are only considered in our study (f). Non-vertical holes are usually machined in a special manner. Curved surface: A group of polygons approximating a curved shape (g).

In the above definition, pocket and slot features can be recognized as special table features with adjacent walls, therefore they are treated in a same manner in the following discussion. A vertical hole feature is considered as a special wall feature in a similar reason. Polygons not used in the form features represent the raw cast surface. They are not machined in the holder fabrication.

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3.3 Basic Processing Flow Our analysis algorithm finds the manufacturability problem of form features in the following 2 steps; Step 1: CAD model of a holder part is modified in consideration of the shape error of the raw cast object. Un-machinable regions on form features occur because of possible interferences between the cutter and the holder part with shape errors (see figure 2). In order to completely detect such interferences, the maximum volume shape of the holder part allowed in the shape error range is computed by “expanding” the CAD model. The detail of the expansion method is given in the next section. Step 2: Based on the expanded CAD model, un-machinable regions on form features are detected. Our developed algorithm [6] is used in the detection. This algorithm extracts the regions by successively applying the inverted offsetting and milling simulations. In our implementation of the algorithm, geometric models in the Z-map representation are used [1]. Since Z-map cannot represent the vertical shape precisely, this algorithm is unable to detect un-machinable regions on wall and hole features. Improvement of the algorithm for precisely analyzing the wall and hole feature case is discussed in section 5.

4 Step1: Modification of Holder Part In this section, the expansion method of the holder part model to obtain its maximum volume shape is explained. A holder model is represented as a set of triangular polygons. They are classified into the following 2 groups; 1. 2.

Polygons representing form features such as tables, walls, slots, pockets and curved surfaces. Other polygons representing the raw cast surface.

Different expansion methods are applied to each polygon group.

4.1 Expansion of Raw Cast Surface The maximum shape of the raw cast surface is represented by offsetting the surface with the possible largest shape error. Since raw cast object is known to have 5 to 10 mm errors, the raw cast surface area of the holder CAD model is offset by 10mm in our implementation. This shape is equivalent to a Boolean union shape of spheres, cylinders and prisms being placed on all polygons of the raw cast surface as follows (see figure 4); • Spheres of radius ε are placed on all vertices of the surface. ε means the maximum shape error of the raw cast object. • On each edge e, a cylindrical pin shape of radius ε is placed so that its center axis and e become coincident. • On each polygonal face p, a prism shape of the same area and thickness of 2ε is placed so that the center plane of the prism and p become coincident.


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Fig. 4 (a) Placement of a sphere on a vertex v, (b) a cylinder on an edge e, and (c) a prism on a triangular polygon p of a raw cast surface model

4.2 Extension of Form Features Form features such as tables and walls are also expanded by the maximum shape error of the raw cast object. Different from the raw cast surface, the surface area of the form feature is machined in the exact shape. For example, horizontal surface area of a table features is machined so that it has the exact flatness and height. Therefore, the “expansion” of a form feature is actually realized as “extension” of the feature surface in its tangential direction. In our study, each form feature is represented as a group of triangular polygons. Since table, slope, slot, pocket, wall and hole features can be recognized as a special type of the curved surface feature, the extending method of a curved surface feature is only explained. As a preparation, each boundary curve of a curved surface feature is traced in counter clockwise order based on the adjacency information between polygons. Edges and vertices on the boundary are indexed as ei and vi in their traced order (see figure 5). The extension of the curved surface in its tangential direction is realized by simply attaching a small quadrilateral and a part circle to each boundary edge and vertex in the following manner; Attachment of small quadrilateral: For each boundary edge ei, a small quadrilateral Qi is attached. Consider a vector ui from vi to vi+1 and the normal vector n of a form feature polygon being adjacent to ei. As a cross product of ui and n, a vector si representing the tangential extending direction of the feature at ei is obtained. Qi is defined by shifting ei in the si direction by ε meaning the maximum shape error. Attachment of small part circle: A boundary vertex vi has two adjacent boundary edge ei-1 and ei. By using the method mentioned above, quadrilaterals Qi-1 and Qi are defined for ei-1 and ei respectively. Consider extending direction vector si-1 for Qi-1 and another vector si for Qi. If cross product of si-1 and si, and the normal vector of the form feature at vi are in the same direction, there is a gap between Qi-1 and Qi as shown in figure 5. This gap is fixed by a part circle Ci whose center point is at vi and containing the vectors si-1 and si, and of radius ε.

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Fig. 5 Definition of quadrilaterals and part circles for extending a curved surface feature

4.3 Resolution of Feature Interferences Table features are usually defined on the top of protrusion shape of the raw cast object. So most table features are surrounded by raw cast surfaces as shown in figure 6. Therefore, the offset shape of the raw cast surface and the extended shape of the table feature often have interferences. Similar problems happen between form features also. For example, a slot feature is defined as a flat surface with its adjacent vertical wall features. When the flat surface part of the slot feature and the wall features are extended, their attached quadrilaterals and part circles have interferences. After the expansion of the raw cast surface and the extension of the form features, these interferences must be resolved. Resolution method is different for (1) feature and raw cast surface interference case and (2) feature and feature interference case.


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Fig. 6 Modification of the offset raw cast surface intersecting the extended table feature

Interference resolution between feature and raw cast surface: The extended shape of the form feature and the offset shape of the raw cast surface are compared, and a part of the offset surface which appears above the extended feature is detected and removed as shown in figure 6.

Fig. 7 Modification of mutually intersecting extended table and extended wall features

Interference resolution between extended form features: These interferences are further classified into the following two cases. Convex intersection: Two extended features intersect so that they make a convex angle at the intersection curve. Concave intersection: Two extended features make a concave intersection curve. In figure 7, a table feature connects two wall features named wall0 and

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wall1. Intersection between the extended table and the extended shape of wall0 organizes a convex intersection. Another intersection between the extended table and the extended shape of wall1 is a concave intersection. In the convex intersection, the extended part of wall0 appearing above the table and the extended part of the table appearing above wall0 are erased. On the other hand, the extended part of wall1 appearing below the table and the extended part of the table appearing below wall1 are erased in the concave intersection. These operations are implemented in our solid modeling system based on the Boolean intersection method between surfaces [10]. Our system has the offset function of the raw cast surface and the feature extension functions also. Z-map is used as the solid object representation format in this system. In the Z-map, the object surface is represented by a height map of vertical segments which are defined on rectangular grids in the XY plane. Therefore, the object surface must have unique z value for every (x, y) grid point in the Z-map representation. Form features on a holder part are machined with a vertical cutter, so their shape basically satisfies this condition. Since the top portion of the raw cast surface only affects the accessibility of the vertical cutter to the form features, Z-map representation is sufficient for defining the effective raw cast surface and its offset result. Vertical features such as walls and holes are exceptions. Handling method of these features is explained in the next section. Input model of a holder part is given to our modeling system to obtain its maximum volume shape. The result shape is recorded in the Z-map format and used in the following cutter accessibility analysis.

5 Step2: Cutter Accessibility Analysis 5.1 Basic Algorithm Based on the maximum volume shape of the holder part, the accessibility of a milling cutter is checked and un-machinable regions on extended form features are extracted. In this subsection, the outline of the accessibility analysis is explained. The detail of the method is given in our prior paper [6]. Our algorithm achieves the cutter accessibility analysis in the following 2 steps; Step 2.1: Compute a cutter path which completely covers the maximum volume model of the holder. The path must be computed so that the cutter moving along the path can engrave the model shape as exact as possible. Such cutter path is easily generated on the inverted offset surface of the model shape (see figure 8(a)). The inverted offset surface is equivalent to the top surface of the result shape of Minkowski sum operation between the maximum volume model and the inverted cutter. Step 2.2: Execute geometric milling simulations using the cutter path obtained in step 2.1 and the cutter model. Milling operation is geometrically equivalent to a Boolean subtraction of the swept volume of the cutter moving along the path from a solid model representing the stock shape. After the simulation, the maximum


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Fig. 8 Un-machinable region extraction method. (a) Minkowski sum operation with an inverted cutter, and (b) milling simulation process.

volume model of the holder and a model obtained as the simulation result are compared. As shown in figure 8(b), an un-machinable region on a form feature is extracted as a region where some material remains on the extended feature surface. Both the inverted offsetting and the milling simulation are very time consuming task. The authors developed a GPU (graphics processing unit) based method for accelerating these computations. In this method, the inverted offsetting and the milling simulation are translated into hidden surface elimination problems of polygon rendering [7]. Once the translation is done, the depth buffer mechanism of GPU can perform the computations very rapidly. Since GPU is now a standard component of most computers, this technology is available with no additional hardware cost.

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Fig. 9 (a) A cutter path for milling a wall feature, and (b) a flat end cutter moving along the path

5.2 Vertical Feature Case The analysis algorithm mentioned above is not suitable for extracting unmachinable regions on form features with vertical surfaces, such as wall and hole features. Remained shape after the milling simulation usually has a vertical pillar like shape as shown in figure 8(b). The remained shape tends to have rather large numerical errors after the complex inverted offsetting and milling simulation. Furthermore, Z-map cannot represent the vertical wall feature and hole feature precisely. Therefore, shape comparison between the vertical features and vertical remained shape is difficult. The authors develop a different method for analyzing the cutter accessibility to wall and hole features. Machining method of a vertical wall feature is standardized in most companies. In this method, a flat end cutter is selected and the cutting edge on its cylindrical side face is used to generate vertical shape. A cutter path for milling a wall feature with this cutter is generated so that the center point of the cutter moves along the offset curve of the boundary of the extended wall feature. Cutter radius is set to the offset value. The cutter moving along the top part of the path is not effective in milling the wall, so only the bottom part of the path is selected as shown in figure 9(a). Side face of a flat end cutter moving along the path can completely scan the wall feature (see figure 9(b)). A vertical hole is usually machined with a drill of the same radius to the hole, or a flat end cutter with smaller radius. In the drilling case, the trajectory path of the drill becomes identical to the center axis of the hole. In the flat end milling case, the same path generation method for milling a wall feature is applicable.


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Fig. 10 (a) Placement of a cutter model. It intersects the maximum volume model of a holder part. (b) Interference resolution by lifting up of the cutter model.

After the path generation, the path is subdivided by inserting many points on the path. The distance between points is set to be 0.1mm in our study. A cutter (a flat end cutter or a drill) model is then placed to each point, and the intersection between the cutter and the maximum volume model of the holder part is checked (see figure 10(a)). Since the Z-map is adopted in our model representation, the intersection check is achieved by simply comparing the end points of Z-map segments and the cutter model. This comparison can be efficiently executed by using the parallel computation capability of GPU. If the cutter and the holder model intersect, some regions on the wall feature are not machinable. Then the cutter is moved upward until the cutter and the holder model do not have any intersections. In this motion, the trajectory of the center point of the cutter is recorded and mapped to the wall feature as shown in figure 10(b). This computation is repeated to all points on the cutter path and the un-machinable region on the wall feature is detected. Un-machinable region on a hole feature is detected in a similar manner.

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5.3 Special Case Analysis Our cutter accessibility analysis method detects the un-machinable region by comparing the maximum volume model of the holder and the milling simulation result. This method cannot detect some un-machinable regions originated in the maximum volume model itself. Figure 11 illustrates this problem. Holder part designer sometimes define a placement of form features as shown in figure 11(a). This figure shows a condition that two table features are connected by a vertical raw cast surface. When these features and raw cast surface are expanded by using our modification method, a shape shown in figure 11(b) is obtained. In this shape, a part of the lower side table feature is covered by the extended upper side table feature so the covered region (a green color region in figure 11(b)) cannot be machined by using a vertical cutter. Such un-machinable region is difficult to detect by our analysis program because the shape shown in figure 11(b) itself is possible to machine. Another trouble case is given in figure 12. Our modeling system uses the Z-map representation for recording the shape data. In the Z-map representation, a placement of table feature and wall feature as shown in figure 12(a) cannot be properly represented because they organize an “overhang” shape. The result shape after the extension of the table and wall features becomes as shown in figure 12(b). In the original model, a part of the table feature exists under the wall feature. Since the vertical milling cutter cannot access such covered region on the table (a green color region in the figure), it remains un-machined. This covered region disappears in the modified model, so our analysis system cannot detect this un-machinable region. In order to overcome these limitations, the authors introduce a function to directly compare the extended shape of the table feature and the maximum volume holder part model. If some regions of the extended table is being contained within the maximum volume model as shown in figure 11(b) and 12(b), such regions are extracted and recorded as the un-machinable regions.

Fig. 11 Un-machinable region on a table feature which is difficult to detect using the method given in figure 8


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Fig. 12 (a) CAD model representation and (b) its modification result using Z-map based modeling system. An un-machinable region disappears in (b).

6 Computational Experiments By using the technology mentioned above, a maximum volume holder model computation program and a cutter accessibility analysis program are implemented using Visual C++, OpenGL, and a GPU language CUDA [9], and some computational experiments are performed. Application results of the programs to a holder CAD model are illustrated in figure 13 and 14. Figure 13 shows a nominal holder model of a stamping die. Its size is 4462mm x 2061mm x 845mm. This part is usually machined with a flat end cutter of radius 40mm. This cutter is attached to a cutter holder of radius 150mm. In the maximum volume model computation and the accessibility analysis, a Z-map model which is defined on a 7000 x 7000 resolution grid in the XY plane is used. Our program can check the cutter accessibility for all features on a holder part at one time, or check the accessibility for each feature in one-by-one manner. In checking all features at one time, whole part shape is represented in a single Zmap model, therefore the gird size of the Z-map becomes 0.42mm for the holder part shown in figure 13. The grid size of the Z-map means the accuracy of the computation. The accuracy is much improved in checking the accessibility for each feature one by one. The maximum size of the table shown in figure 13 is 400mm x 400mm, so the Z-map model accuracy becomes 0.06mm. This accuracy is generally sufficient in our un-machinable feature detection purpose. This method is, however, requires several times more computation time for checking all features compare to the whole shape checking method. In order to efficiently

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Fig. 13 Un-machinable regions on table features in a holder part model

achieve the verification, designers should check the existence of un-machinable regions on all features by using the whole shape checking method at first, then apply the one-by-one checking method to each detected feature to understand the unmachinable regions precisely. A PC with Intel Core2 Duo Processor (3.33GHz) , 3GB memory and NVIDIA GeForce GTX-280 GPU is used in our experiments. For analyzing the cutter accessibility of all features appearing in figure 13, our program needs 14.99 CPU seconds for computing the maximum volume model, and 117.26 CPU seconds for analyzing the cutter accessibilities. 349 un-machinable regions are detected on form features defined on the holder part. 71 regions are on tables, 274 regions are on walls, and 4 regions on slots. The authors compare our computation result to another result manually done by a machining expert. Our result includes all the un-machinable features detected manually. In addition, it can detect some unmachinable regions which are not detected by the expert. In figure 13, all un-machinable regions detected on table features are illustrated in green color. Some large un-machinable regions are specified with white arrows. Close-up picture of an area enclosed by a white rectangle is given in figure 14. Figure 14(a) shows un-machinable regions detected on table features in this area, and (b) shows the regions on wall features. In these figures, detected unmachinable regions are superimposed on the features in the nominal shape. Since un-machinable regions usually exist on the extended part of the features, they sometimes appear in the outside of the nominal features. In the figure, red curves surrounding the features represent the boundary of the extended features.


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(a)

(b)

Fig. 14 Close-up picture of an enclosed part in figure 13. (a) Un-machinable regions on table features, and (b) such regions on vertical wall features.

7 Conclusion In this paper, the authors propose a manufacturability analysis system which can detect un-machinable features caused by the shape errors of raw cast objects. The following 4 technologies are developed for the system; 1. The maximum volume shape of a holder part is computed by expanding the raw cast surface of the part and extending its form features. 2. Expanded raw cast surface and extended form features often have mutual interferences. They are resolved by removing the intersection portions. 3. Un-machinable regions on the form features are extracted by applying the inverted offsetting and the milling simulation to the maximum volume shape.

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4. Un-machinable regions on vertical features are detected by directly checking the intersection between the cutter model and the maximum volume shape. The following is our future research subjects; 1. Reduction of the computation time: Current system requires some minutes in the accessibility analysis. Further improvement of the computation speed is necessary. 2. Displaying method: Current system can display only un-machinable regions detected on form features. This information is not helpful for the designer for understanding how to modify the holder part to resolve the un-machinable regions. Better displaying method which is much informative for the designer must be studied.

References [1] Choi, B.K., Jerard, R.B.: Sculptured Surface Machining, Theory and Applications. Kluwer Academic Publishers, Dordrecht (1998) [2] Cutkosky, M.R., Tenenbaum, J.M.: Toward a computational framework for concurrent design. In: 16th Annual Conference of IEEE Industrial Electronics Society, IECON 1990, pp. 700–706 (1990) [3] Gupta, S.K., Das, D., Regli, W.C., Nau, D.S.: Automated manufacturability analysis: A survey. Research in Engineering Design 9(3), 168–190 (1997) [4] Gupta, S.K., Nau, D.S.: Systematic approach to analyzing the manufacturability of machined parts. Computer-Aided Design 27(5), 323–342 (1995) [5] Hsiao, D.: Feature Mapping and Manufacturability Evaluation with an Open Set Feature Modeler. Ph.D Thesis, Mechanical Engineering, Arizona State University (1991) [6] Inui, M., Miyashita, T.: Hollow Shape Extraction: Geometric Method for Assisting Process Planning of Mold Machining. In: Proc. 2003 IEEE ISATP 2003, pp. 30–35 (2003) [7] Inui, M., Ohta, A.: Using GPU to Accelerate Die and Mold Fabrication. IEEE CG&A Magazine 27(1), 82–88 (2007) [8] Miyakawa, S.: Simultaneous engineering and producibility evaluation method. In: Proc. of the SME International Conference on Application of Manufacturing Technologies (1991) [9] NVIDIA: NVIDIA CUDA Compute Unified Device Architecture, Programming Guide Ver.1.1 (2007) [10] Satoh, T., Chiyokura, H.: Boolean Operations on Sets Using Surface Data. In: Proc. Symp. on Solid Modeling Foundations and CAD/CAM Applications, pp. 119–126 (1991) [11] Subramanyan, S., Lu, S.: The impact of an AI-based design environment for simultaneous engineering on process planning. International Journal of Computer Integrated Manufacturing 4(2), 71–82 (1991)

Automatic Determination of Fixturing Points: Quality Analysis for Different Number of Points and Friction Values Jan Rosell, Raúl Suárez, and Francesc Penalba

Abstract. This paper copes with the automatic determination of fixturing points on 2D and 3D free-form objects, for any number of fixturing points and a variable friction coefficient at the contacts. An approach is proposed that, starting from an initial set of points, successively finds a better set by changing only one point at a time following an heuristic search procedure that uniformly explores the object surface. A software tool that implements this approach is also presented. This tool also allows to analyze the quality of any given set of fixturing points, which has allowed us to determine how many points are necessary for a given coefficient of friction in order to fix 2D and 3D objects with a given quality. The tool has been released as open software.

1 Introduction A key point in a manufacturing process is the proper fixturing of objects when they are going to be processed in any way, or some particular actions must be done on them. There is a number of well known examples, like for instance polishing, drilling, or just performing an assembly of subparts to form a more complete product, among several others. In this situations there is always at least one part that must keep its position despite the application of external forces on it, in order to successfully perform the desired action. There are several works dealing with the problem of object fixturing, considering different particular conditions and/or constraints, including a number of works presented in the field of grasping and manipulation, which has several points in common with the problem of fixturing. Jan Rosell · Raúl Suárez · Francesc Penalba Institute of Industrial and Control Engineering (IOC), Technical University of Catalonia (UPC), Barcelona, Spain e-mail: [email protected]

This work was partially supported by the Spanish Government through the projects DPI2007-63665 and DPI2008-02448.

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J. Rosell, R. Suárez, and F. Penalba

Relevant concepts in this field are the form-closure property (the position of the fixtures/fingers ensures the object immobility) and force-closure property (the forces applied by the fixtures/fingers ensure the object immobility) [2]. The force-closure constraint is more frequently required in grasping, since the movement of the object makes its own weight to act as an external perturbation, while the form-closure constraint is more frequently required in fixturing, where the object usually lies in a stable position while no operation in being performed on it. Some relevant works dealing with grasping and fixturing of objects based on this property are given below in Section 2. In this work we present a tool to decide which is the most convenient way to restrict the position of an object assuring a desired minimum quality in terms of the forces that the object can resist without loosing the position. We have extended a previous work [22] and made an implementation that allows the search and analysis of fixturing points on the object. The idea is to visualize the quality of potential fixturing configurations under different conditions, like the number of contact points and the friction coefficient at those points, and use this information to decide how to secure the object. The approach is valid for 2D and 3D free-form objects. The paper is organized as follows. After this introduction, Section 2 presents the approach used to find force and form closure fixturings and to evaluate their quality. Section 3 describes the implemented tool (software) developed to search and analyze object fixturings. Section 4 shows some application examples in order to illustrated the approach. Finally Section 5 summarizes the work, presents some conclusions and discusses future work and potential improvements.

2 Fixturing Search and Evaluation How to constrain the position of an object depends on several factors, which determine the approaches followed by different researchers. The most relevant ones are listed here, together with a review of the most used quality measures that evaluate this constraint satisfaction in terms of the forces that the object can resist without loosing the position. Afterwards, the proposed approach is presented, which is a generalization of the work presented in [22].

2.1 Related Background How to constrain an object in a desired position depends on a number of factors, being the most relevant: the dimension of the object, i.e. 2D or 3D, the object shape, i.e. polyhedral or non-polyhedral, the type of contact between the fixtures (or fingers) and the object, i.e. frictionless, frictional or soft contact, and the number of contacts, which for arbitrary 3D objects must be equal or larger than 2 when soft contacts are considered, equal or larger than 4 for frictional contacts (exceptionally, 3 contacts may be enough for some particular objects), and equal or larger than 7 for frictionless contacts. See [3] for a review of these factors. These different cases are addressed in several relevant works, considering, for instance, 2D

Automatic Determination of Fixturing Points

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polygonal objects [11], 2D non-polygonal objects [5], 2D discrete objects [18], 3D polyhedral objects [19, 6], 3D non-polygonal objects [24, 23], and 3D discrete objects [12, 17, 20]. Arbitrary shaped objects are frequently modeled with a finite (but large) number of points, either using clouds of points as samples of the object surface or any type of mesh. These models are quite convenient when the object boundary is obtained using range sensors, or some vision systems based on structured light [1, 4], and they can also easily be obtained from any other representation. In this work we consider the boundary of a 3D object to be described by a triangular mesh, while a 2D object boundary is directly described by a finite sequence of discrete points.

2.2 Quality Measures Several different quality measures have been presented in the literature to evaluate the performance of a given fixture or grasp. See [21] for a survey on grasp quality measures. The quality measures that take into account the object properties (shape, size, weight), friction constraints and form and force closure conditions to quantify the grasp quality, can be classified into three subgroups. The first two groups do not consider limitations in the magnitudes of the forces applied at the contact points, one group considers only algebraic properties of the grasp matrix (for instance the value of its minimum singular value that indicates how far is the grasp from a singular configuration [10]), and the other group considers geometric relations in the grasp (for instance the shape [8] and the area [16] of the polygon defined by a three contact point fixture). The third group considers limitations in the magnitudes of the forces applied to constrain the object, thus being more realistic for practical applications. The quality measures used in this work belong to this third group, although constraints derived from the indeterminate friction forces in a quasi-static analysis [13] are not included. Given the forces that can be applied on the object at the contact points, the produced wrenches on the object are known, and they are used to compute the following quality measures: a) The radius of the largest hypersphere centered at the origin of the wrench space and fully contained in the Convex Hull of the wrenches that can be applied on the object at the contact points [7, 9], which indicates the maximum wrench that the constrained object can resist independently of the wrench direction. This measure depends on the reference point used to compute the torques. b) The volume of the the Convex Hull of the wrenches that can be applied on the object at the contact points [14], which gives an idea of the amount of wrenches that the object can resist, and is constant independently of the reference system used to compute the torques.

2.3 Implemented Approach The approach used to compute a set of fixturing points and to evaluate its quality is a generalization of the work presented in [22], which deals with the case of seven

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frictionless contact points for 3D discrete objects. That work is extended to allow the application to 2D and 3D objects, and using any number of contacts, either frictionless or frictional. Some other added features are described below. The main algorithm, valid for 2D and 3D objects and any number of frictionless or frictional contacts, is as follows: Step 1: Step 2: Step 3: Step 4: Step 5: Step 6:

Generate an initial set G of m fixturing points and evaluate its quality. Select another point p j on the object surface. Select a particular point pi ∈ G Evaluate the resultant quality when pi is replaced by p j in G. If the quality grows then update G replacing pi by p j . While a finishing condition is not satisfied go to Step 2.

The generation of the initial set G of m fixturing points in Step 1, as well as the other points in Step 2, is done using a sampling procedure that tries to pick points uniformly distributed over the object surface. Random and deterministic sampling algorithms were used for this purpose. The first point of G is randomly selected, and the remaining m − 1 points of G and the rest of the points in Step 2 are either randomly selected or selected maximizing the distance to the already selected points, in this latter way the object surface is better uniformly sampled (Fig. 1). The distance between points can be measured in different ways as, for instance, using a Euclidean distance between any two points or using the number of points in the mesh between them (details about the implemented solutions are given in next section). This generation of samples is iteratively repeated until a termination condition is satisfied. The evaluation, in Steps 1 and 4, of the fixturing quality produced by the set of contact points G is computed using any of the two criteria presented in Subsection 2.2.

Fig. 1 Illustration of the deterministic sampling (top) and random sampling (bottom) on the object surface of a pawn model for 20, 30 and 40 samples from left to right, respectively. Deterministic sampling obtains a better uniform coverage of the object surface.


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The selection of a particular point pi ∈ G in Step 3 is done such that, once a new point p j is selected on the object surface, the direction of the wrench wi produced by the normal force applied on pi is the closest to the direction of the wrench w j produced by the normal force applied on p j . This criterion tends to minimize the change in the directions of the potential wrenches applied on the object and facilitates the convergence of the algorithm. Step 5 is straightforward, and, finally, the finishing condition in Step 6 can be any of the followings: • • • •

A given desired minimum quality is obtained. A given number of steps without improving the quality were performed. A given number of points on the object surface were visited. All the points on the object surface were visited.

3 A Tool to Analyze the Fixtures There exists a powerful tool, Graspit! [15], that is focused on grasp planning, providing procedures to find the best grasp of a given object with a given mechanical hand. In our work we are interested in analyzing some properties of fixturings only from the object point of view, in particular the relation between the number of points, the friction coefficients at the contacts and the fixturing quality that can be obtained. For this reason, a tool called Grasp Analysis Tool (GAT) has been implemented to find fixturing or grasping points for a given object following the algorithm presented in the previous section. The tool can also be used to evaluate the quality of any set of given fixturing or grasping points. It has basically been implemented with an analysis aim and, thus, the user can define many parameters related to the object models used, the type of fixtures, the quality measures or some parameters of the search algorithm. They are detailed in the following subsections. The software package can be downloaded from http://iocnet.upc.edu/usuaris/JanRosell/GAT/GAT.html.

3.1 Object Models The Grasp Analysis Tool works for free-form objects in two and three dimensions: 2D objects are defined as a closed line described by a sequence of points; 3D objects are defined as a closed volume described with a triangular mesh. The segments defined by two consecutive points in 2D, or the triangles in 3D, are called elements. Their geometric center define the candidate fixturing or grasping points. Therefore, the search algorithm obtains better results with models composed of many uniform elements. The tool has an option that allows to refine the models by subdividing all their segments or triangles as illustrated in Fig. 2. Also, a parameter λ is defined to scale the objects. Assuming unitary forces at the contact points, the parameter λ is used to scale the torques, i.e. wi = (fi , λ τ i ).

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Fig. 2 Model refinement process on a dodecahedron. From left to right, model composed of 60, 240 and 960 triangles, respectively.

3.2 Type of Fixtures Fixtures vary as a function of the number of fixturing points and as a function of the force directions that can be exerted at them, which is determined by the friction coefficient at the contacts. In the Grasp Analysis Tool, the effect of friction is introduced using the Coulomb friction model, considering the friction coefficient μ equal at all the contact points. For the 3D case, the friction cone is approximated by a polyhedral convex cone with eight sides. The frictionless option is also available. For the frictionless case the number of points ranges from 4 and 7 for the 2D and 3D cases, respectively, up to the number of elements in the object model. When friction is considered, the minimum number of points is set to 3 and 4, respectively. Fig. 3 shows the interface devoted to the configuration of these parameters.

Fig. 3 Interface to determine the type of fixture: number of points and friction coefficient


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3.3 Quality Measures The two quality measures used have been described in Section 2.2. A combination of them has also been implemented as a third option, although it is not used in the search algorithm shown in Section 2.3 but only provided for evaluation purposes. They are labelled as: • Q1 : The radius of the maximum hypersphere. • Q2 : The volume of the Convex Hull. • Q3 : The ratio between Q1 and Q2 .

3.4 Parameters of the Searching Algorithm The Grasp Analysis Tool tool allows the searching algorithm to be run with different sampling strategies and with different distance measures: a) Sampling strategies: Deterministic or random sampling strategies can be chosen, as illustrated in Fig. 4, being the number of points to be sampled also variable. The manual selection of the candidate points is also possible.

Fig. 4 Interface to select the desired sampling strategy and the distance measure to be used

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Fig. 5 Discrete distance from a given triangle (white) to the other triangles in the mesh, computed using standard neighborhood (left) and extended neighborhood (right)

For objects with few elements considered as potential fixturing points, the algorithm can be run in an exhaustive way, i.e. all the combinations are tested and the one with the best quality is chosen. b) Distance measure: Distance between two elements is computed by the propagation of the distance between neighbor elements, thus, several alternatives can be chosen, as illustrated in Fig. 4. First, for 3D models two type of neighborhood can be selected: a) Standard neighborhood: two triangles are considered neighbors if they share an edge; b) Extended neighborhood: two triangles are considered neighbors if they share at least one vertex (Fig. 5). Second, the distance between neighboring triangles can be defined in two ways: a) Discrete distance: neighboring triangles are at a distance one; b) Euclidean distance: the distance between neighboring triangles is computed as the Euclidean distance between their centers.

4 Analysis of Fixturing Quality: Examples This section uses the GAT tool to analyze how the fixturing quality depends on the number of fixturing points and on the friction coefficient. The examples are based on the application of the searching algorithm on 2D and 3D models with the following parameters (see Subsections 3.3 and 3.4): • • • • •

Quality measure: Q1 . Sampling sequence: Deterministic. Distance measure: Euclidian distance combined with extended neighborhood. Friction values: 0.01, 0.05, 0.10, 0.15, 0.20 and 0.25. Number of fixturing points: from 3 to 11 for the 2D case and from 4 to 11 for the 3D case.

Since the search algorithm is heuristic, no optimal result can be guaranteed. Therefore, each example has been run three times starting each time with a different element on the object surface. The chosen starting elements are: a) the closest element to the geometric center of the object; b) the furthest element to the geometric center of the object; c) a randomly selected element. For each example, the quality obtained by the algorithm for each friction value and for each number of fixturing points is graphically reported. This quality is the maximum obtained by running the algorithm from the three considered starting points.


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4.1 2D Examples Two 2D examples have been considered: a rectangle and an ellipse. In both cases, the algorithm has been run until all the points on the object perimeter have been visited. The rectangle has an aspect ratio 3 × 1. The initial model, composed of eight uniform elements, has been refined up to 256 elements, resulting each element with a size lower than the 0.4% of the total perimeter. The ellipse has an aspect ratio 2 × 1. The model is composed of 400 non-uniform elements, being their size lower than the 0.35% of the total perimeter. Figures 6 and 7 show the results. As expected, it can be seen that the quality increases with the number of fixturing points and with the friction coefficient. In both cases this increase is not relevant for more than 6 fixturing points, being even for the ellipse not much relevant from 4 fixturing points. The increase in the friction coefficient is, on the other hand, always relevant, irrespective of the number of fixturing points used.

Fig. 6 Experiment results with the Rectangle: (top) quality Q1 vs. number of fixturing points for different friction coefficients; (bottom) quality Q1 vs. both number of fixturing points and friction coefficients

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Fig. 7 Experiment results with the Ellipse: (top) quality Q1 vs. number of fixturing points for different friction coefficients; (bottom) quality Q1 vs. both number of fixturing points and friction coefficients

4.2 3D Examples Three 3D examples have been considered (Fig. 8): two regular polyhedra (a tetrahedron and a dodecahedron), and an irregular object (a pawn). For the tetrahedron, the algorithm has been run until all the points on the object surface have been visited. For the other two examples the number of visited points has been limited due to the computational time needed for the complete exploration, and of the very slow

Fig. 8 3D examples


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Fig. 9 Experiment results with the Tetrahedron: (top) quality Q1 vs. number of fixturing points for different friction coefficients; (bottom) quality Q1 vs. both number of fixturing points and friction coefficients

increase in the quality that is obtained once a representative number of points have been visited. The initial model of the tetrahedron, composed of only four triangles, has been refined up to 256, resulting each triangle with an area lower than the 0.4% of the total area. The initial model of the dodecahedron, composed of 60 triangles, has been refined up to 960, resulting each triangle with an area lower than the 0.15% of the total area. The maximum number of sampled triangles was set to 200. The initial model of the pawn, composed of 304 triangles, has been refined up to 1216, resulting each triangle with an area lower than the 0.4% of the total area. The maximum number of sampled triangles was set to 300. Figures 9, 10 and 11 show the results for the tetrahedron, the dodecahedron and the pawn, respectively. As in the 2D examples, the quality increases with the number of fixturing points and with the friction coefficient. For the tetrahedron, the grasping quality presents a staircase shape with respect to the number of fixturing points, i.e. there are flat regions between 4 and 6 points and between 8 and 10. Therefore it makes nonsense to use 5 or 6 points instead of

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Fig. 10 Experiment results with the Dodecahedron: (top) quality Q1 vs. number of fixturing points for different friction coefficients; (bottom) quality Q1 vs. both number of fixturing points and friction coefficients

4 since the quality is nearly the same, and for the same reason it makes nonsense to use 9 or 10 points instead of 8. For the dodecahedron there is a very important increase of quality when incrementing the number of fixturing points from 5 to 7, which motivates the use of a number of fixturing points equal to or larger than 7. For the pawn it can be observed that for low friction coefficients there is a considerable quality step between 6 and 7 points, as expected since seven points are required for the frictionless case. Therefore for low friction coefficients the reasonable number of fixturing points is 7 or more. On the other hand, for high friction coefficients the behavior of the quality is almost linear with the number of fixturing points, from 4 up to 9 points. This suggests the use of as many points as possible in this range. In all cases, there is a linear increase as a function of the friction coefficient, irrespective of the number of fixturing points, although this linearity is not so clear for the case of the pawn. Then, the quality is always directly increased by an increase in the friction coefficient.


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Fig. 11 Experiment results with the Pawn: (top) quality Q1 vs. number of fixturing points for different friction coefficients; (bottom) quality Q1 vs. both number of fixturing points and friction coefficients

5 Conclusions This paper has analyzed how the fixturing quality of 2D or 3D free-form objects depends on the number of fixturing points and on the friction coefficient at those points. Fixturing points are found by an heuristic algorithm previously proposed by the authors that has been generalized to both 2D and 3D objects, to friction or frictionless contacts, and to a variable number of fixturing points. A software tool has been implemented to automate this analysis. The results allow to select in each case the minimum number of fixturing points and friction coefficient required to achieve a given desired minimum quality.

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References 1. Alexa, M., Behr, J., Cohen, D., Fleishman, S., Levin, D., Silva, C.: Computer and rendering point set surfaces. IEEE Trans. Visualization and Computer Graphics 9(1), 3–15 (2003) 2. Bicchi, A.: On the closure properties of robotic grasping. Int. J. Robotics Research 14(4), 319–344 (1995) 3. Bicchi, A., Kumar, V.: Robotic grasping and contact: A review. In: IEEE Int. Conf. on Robotics and Automation, pp. 348–352 (2000) 4. Campbell, R., Flynn: A survey of free-form object representation and recognition techniques, computer vision and image understanding. Computer Vision and Image Understanding 81, 166–210 (2001) 5. Cornellà, J., Suárez, R.: On computing form-closure grasps/fixtures for non-polygonal objects. In: IEEE Int. Symp. on Assembly and Task Planning, pp. 138–143 (2005) 6. Ding, D., Liu, Y., Wang, S.: Computation of 3-D form-closure grasps. IEEE Trans. Robotics and Automation 17(4), 515–522 (2001) 7. Ferrari, C., Canny, J.: Planning optimal grasps. In: IEEE Int. Conf. on Robotics and Automation, pp. 2290–2295 (1992) 8. Kim, B., Oh, S., Yi, B., Suh, I.: Optimal grasping based on non-dimensionalized performance indices. In: IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, pp. 949–956 (2001) 9. Kirkpatrick, D., Mishra, B., Yap, C.: Quantitative Steinitz’s theorem with applications to multifingered grasping. J. Discrete and Computational Geometry 7(3), 295–318 (1992) 10. Li, Z., Sastry, S.: Task-oriented optimal grasping by multifingered robotic hands. In: IEEE Int. Conf. on Robotics and Automation, pp. 389–394 (1987) 11. Liu, Y.: Computing n-finger form-closure grasps on polygonal objects. Int. J. Robotics Research 19(2), 149–158 (2000) 12. Liu, Y., Lam, M., Ding, D.: A complete and efficient algorithm for searching 3-D form closure grasps in the discrete domain. IEEE Trans. Robotics 20(5), 805–816 (2004) 13. Maeda, Y., Oda, K., Makita, S.: Analysis of indeterminate contact forces in robotic grasping and contact tasks. In: IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, pp. 1570–1575 (2007) 14. Miller, A., Allen, P.: Examples of 3D grasp quality computations. In: IEEE Int. Conf. on Robotics and Automation, pp. 1240–1246 (1999) 15. Miller, A., Allen, P.K.: Graspit!: A versatile simulator for robotic grasping. IEEE Robotics and Automation Magazine 11(4) 16. Mirtich, B., Canny, J.: Easily computable optimum grasps in 2D and 3D. In: IEEE Int. Conf. on Robotics and Automation, pp. 739–747 (1994) 17. Niparnan, N., Sudsang, A.: Fast computation of 4-fingered force-closure grasps from surface points. In: IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, pp. 3692–3697 (2004) 18. Niparnan, N., Sudsang, A.: Computing all force-closure grasps of 2D objects from contact point set. In: IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, pp. 1599–1604 (2006) 19. Ponce, J., Sullivan, S., Sudsang, A., Boissonat, J., Merlet, J.: On computing fourfinger equilibrium and force-closure grasps of polyhedral objects. Int. J. Robotics Research 16(1), 11–35 (1997)


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20. Roa, M., Suárez, R.: Finding locally optimum force-closure grasps. J. Robotics and Computer-Integrated Manufacturing 25(3), 536–544 (2009) 21. Roa, M., Suárez, R., Cornellà, J.: Revisión de medidas de calidad para la prensión de un objeto. Revista Iberoamericana de Automática e Informatica Industrial 5(12), 66–82 (2008) 22. Suárez, R., Rosell, J.: Searching form-closure fixturing points on objects described by triangular meshes. In: IEEE Int. Symp. on Assembly and Manufacturing, pp. 7–12 (2007) 23. Zhu, X., Ding, H.: Planning force-closure grasps on 3-D objects. In: IEEE Int. Conf. on Robotics and Automation, pp. 1258–1263 (2004) 24. Zhu, X., Wang, J.: Synthesis of force-closure grasps on 3-D objects based on the Q distance. IEEE Trans. Robotics and Automation 19(4), 669–679 (2003)

Contact Trajectories for Regrasp Planning on Discrete Objects Máximo A. Roa and Raúl Suárez

Abstract. Manipulation tasks, in general, require a grasp change on the object during its execution. The manipulation problem can be solved by simply rolling or sliding the fingers on the object surface, the so-called regrasping approach. This paper provides an algorithm for regrasp planning of 2D and 3D discrete objects, such that the regrasp trajectory of each contact ensures a force-closure grasp (i.e. a grasp that resists external disturbances) while the regrasp motion is performed. The proposed approach takes advantage of a sampling-based method that quickly explores the grasp space, and relies on the use of independent contact regions and non-graspable regions, which provide large regions of the force-closure or non force-closure subspaces starting from a single sample. Application examples are included to show the relevance of the results.

1 Introduction A manipulation problem appears when an object grasped by a multi-fingered hand needs a grasp change during the execution of a task; it implies the hand ability to change the position and orientation of the manipulated object from an initial to a final position. The final position can be achieved by simply moving the object inside the hand’s workspace, changing the position of the hand joints. The range of possible Máximo A. Roa Institute of Robotics and Mechatronics, German Aerospace Center (DLR e.V.) D-82234, Wessling, Germany e-mail: [email protected] Raúl Suárez Institute of Industrial and Control Engineering (IOC), Technical University of Catalonia (UPC), 08028 Barcelona, Spain e-mail: [email protected]

This work was partially supported by the Spanish Government through the projects DPI2007-63665 and DPI2008-02448.

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movements that can be imparted on the object without changing the actual grasp is determined by the physical limits in the finger joints and the possible collisions between the fingers and the object. If the final position is not achievable in this way, then the contacts between the fingers and the object must be changed at some point during manipulation, and at least one contact point must be located in a different position; in this way the object can achieve a wider range of positions. Under this assumption, two different ways of manipulation can be established: finger gaiting and regrasping. Finger gaiting (or finger repositioning) involves the relocation of one or more fingers on the object surface while keeping the force-closure (FC) grasp with the remaining fingers (at least 2) [10]. The change of a grasp from n to n − 1 fingers involves a change in the problem conditions, as the degrees of freedom of the handobject system may increase when one contact is lost. The sequence of movements starts with an n − 1 finger grasp. The object is rotated without changing the contact points until one of the fingers reaches its workspace limits, then, a redundant (free) finger must be located to generate a grasp that allows lifting the limiting finger such that a new n − 1 FC grasp is obtained [7]. Another approach simply changes between different FC grasps by using one or more free fingers, rotating the object until the desired position is reached [9]. On the other hand, the regrasping approach (or multi-fingered manipulation) solves the manipulation problem by simultaneously using all the available fingers; the positions of the fingers can only be changed by rolling or sliding them along the object surface. The theoretical basis for rolling contacts has been established considering the finger-object system [10] and also including the hand kinematics [8]. Manipulation by rolling has been simulated, even using wheeled fingertips [11], but real applications are limited to simple experimental setups such as a 2-finger hand manipulating a ball [6], mainly due to control and stabilization problems, as well as limitations in the workspace of the fingers [1]. Finger sliding is a process that repositions the fingers by sliding them along the object surface; the theoretical basis for this process has been studied [2, 5], but it is hard to be mechanically implemented as the fingers must touch the surface during all the sliding movement [13], which requires tactile sensors with high accuracy and a very controlled hand dynamics. Assuming that the manipulation is performed at low velocities, then the interaction forces between the fingers and the object are dominant compared to the inertial forces, and the manipulation can be considered as quasi-statical, which simplifies the problem formulation. A dexterous manipulation planner that takes advantage of the quasi-statical formulation for 3D smooth objects has already been proposed [3]. However, computation of regrasp trajectories for general 3D objects has only been recently tackled. When dealing with 3D arbitrary shaped objects, a common approach to describe their surface is by using a cloud of points or a triangular mesh. A method was proposed to avoid dealing with the large amount of data involved in these representations; the approach starts with a triangular mesh, which is simplified and used to build a regrasp roadmap [12].

Contact Trajectories for Regrasp Planning on Discrete Objects

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This work discusses the problem of searching the trajectories for the fingertips on an object surface, in order to change from an initial FC grasp to a final desired one while ensuring the FC condition (i.e. ensuring the resistance to external disturbances) during the finger movements. A solution to the problem is presented based on the concepts of independent contact regions (ICRs) and non-graspable regions (NGRs) [15]. ICRs are defined such that the positioning of a finger in each ICR ensures an FC grasp, independently of the exact position of each finger. NGRs are defined such that a finger contact in each NGR always produce a non-FC grasp, independently of the exact position of each finger. The approach used in this work focuses only on the object geometry and the FC property to find the trajectories for the fingertips on the object surface, i.e. it is object-centered. The kinematics of the grasping device is not considered. It is assumed that the manipulation is performed at low velocities, therefore the manipulation can be considered quasi-statical. The rest of the paper is organized as follows. Section 2 provides a background for the regrasp planning problem. Section 3 describes the approach proposed to plan a regrasp movement on a discrete object, and discusses the problems that appear when the approach is applied to 3D objects. Section 4 shows two examples to illustrate the approach, and, finally, Section 5 presents the conclusions of the work.

2 Background This section presents the assumptions regarding the object modeling and the type of contacts considered, as well as a description of some relevant basic concepts used in the new developments, like the Independent Contact Regions and Non-Graspable Regions and their representation in the grasp space, which are key points in order to improve the efficiency and allow a practical implementation of the proposed approach.

2.1 Assumptions The following assumptions are considered in this work. There is a frictional punctual contact between each finger and the object, with friction being modeled according to Coulomb’s law. The object surface is discretized with a large enough set Ω of points pi , whose positions are described by one or two parameters u for 2D or 3D objects, respectively. The normal direction nˆ i pointing toward the interior of the object at pi is known. Besides, each point is connected with a set of neighboring points forming a mesh of interconnected points on the object surface.

2.2 Independent Contact Regions and Non-graspable Regions Independent contact regions and non-graspable regions are defined on the object surface in such way that a finger located in each ICR or NGR, independently of

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O ICR1 p1

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Fig. 1 ICRs for a discretized ellipse: a) FC grasp in the wrench space (the convex hull contains the origin O); b) ICRs on the ellipse

the exact finger position, always ensures that an FC or non-FC grasp is obtained, respectively. Fig. 1 shows an example of an FC grasp on a discretized ellipse and in the wrench space; it also shows the ICRs for each one of the 4 grasping points on the ellipse. 3,920 different FC grasps can be obtained from the possible combinations of finger positions inside the ICRs. Fig. 2 shows a 4-finger non-FC grasp for the ellipse in the wrench space and on the ellipse boundary. For a non-FC grasp, different sets of non-graspable regions can be computed [15]; each set is called an NGRH. For the example in Fig. 2, NGRH1 and NGRH2 allow 44,100 and 2,313,441 different non-FC grasps, respectively. Algorithms to compute ICRs and NGRHs have been already presented in previous works [14, 15].

O p2 F2

NGRH3 |H1 = NGRH4 |H1 F1 p4

NGRH1 |H2 = NGRH2 |H2 = p3

NGRH1 |H1 = NGRH2 |H1

= NGRH3 |H2 = NGRH4 |H2

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p1

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Fig. 2 Sets of NGRs for a discretized ellipse: a) Non-FC grasp in the wrench space (the convex hull does not contain the origin O), b) First set of NGRs (NGRH1 ); c) Second set of NGRs (NGRH2 )

2.3 Grasp Space An n-finger grasp G is described by the set of parametersui that define the positions of the fingers on the grasped object surface, i.e. G = u1 , . . . , u p , with p = n for 2D objects and p = 2n for 3D objects. The p-dimensional space representing


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the position of the possible contact points defined by u1 , . . . , u p is called the grasp space G. The grasp space G is divided into two complementary subsets: the FC space, formed by the points that represent FC grasps, and the non-FC space, whose points represent non-FC grasps. Fig. 3 shows the grasp space G for an ellipse discretized with 64 points using 3 frictional fingers (i.e. each point of G defines 3 contact points on the ellipse). The grasp space G contains 643 = 262, 144 grasps, with 12.1% being FC grasps and 87.9% being non-FC grasps, as shown in Fig. 3b with dark and light colors, respectively. This ellipse will be used in this work to illustrate the proposed approach for solving the regrasp problem.

u=1

a)

b)

Fig. 3 Grasp space for a 2D object with 3 frictional contacts: a) Discretized ellipse; b) Grasp space

The grasp space G has some symmetries, as any grasp G = u1 , . . . , u p accounts for K different grasps, where K = n! is the total number of possible permutations of the fingers on the object while keeping the same contact points, i.e. the fingers may change their positions with all the other fingers without changing the contact points and the obtained grasps on the object are the same (as long as there are no specific assignments of the fingers to the contact points). For instance, Fig. 4 shows the 6 symmetrical points for a 3-finger frictional grasp of a 2D object. The grasp space is actually divided in 6 sectors or subspaces, symmetrical with respect to each other. The 6 subspaces are also shown in Fig. 4. The ICRs computed on the boundary of the object correspond to an axis-aligned region in the grasp space, hereafter called BI region, which encloses a number of FC grasps. Due to the symmetry described above, the ICRs computed for one grasp are actually mapped to K axis-aligned regions BI in the grasp space, as shown in Fig. 5. A 3-finger grasp is used in the example to allow a graphical representation of the grasp space, which is 3-dimensional for this case. The NGRHs also correspond to axis-aligned regions, hereafter called BN regions, that enclose a number of non-FC grasps in the grasp space. Thanks to the symmetry of G, the NGRHs computed for a non-FC grasp are mapped to K axis-aligned regions BN, as shown in Fig. 6b for the non-FC grasp shown in Fig. 6a. Note that both the BI and BN regions are stored by using 2p parameters, representing the lower and upper limit of the correspondent box along each axis of G.

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M.A. Roa and R. Suárez f3 u = 49

G1 = {7, 27, 49}

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u=1 u=7

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Fig. 4 Symmetries in the grasp space: a 3-finger frictional grasp of an arbitrary 2D object provides 6 points in the grasp space. The symmetrical sectors are highlighted in each figure.


a)

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b)

Fig. 5 ICRs: a) An FC grasp with the corresponding ICRs on the discretized ellipse; b) Correspondent BI regions in the grasp space

a)

b)

Fig. 6 NGRHs: a) A non-FC grasp on the discretized ellipse; b) Correspondent BN regions in the grasp space

3 Regrasp Planning The regrasp planning problem is formulated as follows: given an initial and a final FC grasps, Gi and G f respectively, find a trajectory for each finger contact on the object surface that allows the grasp change while continuously keeping the FC property (i.e. ensuring the resistance to any external disturbance appeared during the regrasp process). The sequence of movements corresponds to a path between the points Gi and G f in the grasp space G such that all the points in the path are FC grasps. Since a grasp is a combination of n discrete points on the object, the p-dimensional grasp space is discretized to represent the potential grasps. This requires a parametrization of the object surface, which should allow an easy way to identify and label the position of the contact points.

3.1 Parametrization The simplest way to obtain an object discretization is the creation of an uniform grid based on an ordered numeration of the points that represent the boundary of

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the object. This numeration is straightforward for 2D objects, as their boundary is a closed curve and the discrete points on the boundary can be uniquely identified by a single parameter u. The parameter that identifies each point is an ordinal number that starts from an arbitrary origin where u = 1. This numbering procedure produces a well-ordered set, where the neighboring relations (required to compute the ICRs) are obtained very easily: a point with code ui has two neighbors, ui+1 and ui−1 . The exceptions are the points u = 1 and u = N, neighbors in the physical space but not in the ordered set; this can be solved readily by identifying them as neighbors in the parameter space. A similar parametrization for 3D objects can be obtained by using a special subset of 3D objects called superquadrics, which are mainly used for solid object modeling and scene representation, and to generate 3D solids from an unstructured cloud of points [4]. There are four kind of superquadric surfaces: superellipsoids, supertoroids, and superhyperboloids of one or two sheets, but only the first two define closed surfaces. Superellipsoids are defined as ⎞ a1 cosε1 φ cosε2 η −π /2 ≤ φ ≤ π /2 s(φ , η ) = ⎝ a2 cosε1 φ sinε2 η ⎠ , −π ≤ η < π a3 sinε1 φ ⎛

(1)

with the parameters a1 , a2 and a3 being the size factors along the three coordinate axes, and ε1 , ε2 the parameters that determine the shape of the superellipsoid. The exponentiation with εi is a signed power function defined as cosεi φ = sign(cos φ ) |(cos φ )|εi . This compact representation allows the generation of a large amount of shapes, as shown in Fig. 7. In order to get convex shapes, the parameters should be ε1 ≤ 2, ε2 ≤ 2. Supertoroids are defined as ⎞ a1 (a4 + cosε1 φ ) cosε2 η −π ≤ φ < π s(φ , η ) = ⎝ a2 (a4 + cosε1 φ ) sinε2 η ⎠ , − π ≤η 0 that is determined as a function of the manufacturing technologies and the employed resources. A task j is assigned to a single station k. Each station k has thus assigned a subset of tasks Sk (Sk ⊆ V ), called its workload. Each task j has a set of direct predecessors, Pj , which must be accomplished before starting it. These constraints are normally represented by means of an acyclic precedence graph, whose vertices stand for the tasks and where a directed arc (i, j) indicates that task i must be finished before starting task j on the production line. Thus, if i ∈ Sh and j ∈ Sk , then h ≤ k must be fulfilled. Each station k presents a station workload time t(Sk ) that is equal to the sum of the tasks’ lengths assigned to the station k. SALBP [15] focuses on grouping tasks in workstations by an efficient and coherent way. There is a large variety of exact and heuristic problem-solving procedures for it [16]. The need of introducing space constraints in the assembly lines’ design is based on two main reasons: (a) the length of the workstation is limited in the majority of the situations, and (b) the required tools and components to be assembled should be distributed along the sides of the line. Hence, an area constraint may be considered by associating a required area a j to each task j and an available area Ak to each station k that, for the sake of simplicity, we shall assume it to be identical for every station and equal to A : A = max∀k∈{1..n}{Ak }. Thus, each station k requires a

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station area a(Sk ) that is equal to the sum of areas required by the tasks assigned to station k. This leads us to a new family of problems called TSALBP in [2]. It may be stated as: given a set of n tasks with their temporal t j and spatial a j attributes (1 ≤ j ≤ n) and a precedence graph, each task must be assigned to a single station such that: (i) every precedence constraint is satisfied, (ii) no station workload time (t(Sk )) is greater than the cycle time (c), and (iii) no area required by any station (a(Sk )) is greater than the available area per station (A). TSALBP presents eight variants depending on three optimisation criteria: m (the number of stations), c (the cycle time) and A (the area of the stations). Within these variants there are four multiobjective problems and we will tackle one of them, the TSALBP-1/3. It consists of minimising the number of stations m and the station area A, given a fixed value of the cycle time c. We chose this variant because it is quite realistic in the automotive industry since the annual production of an industrial plant (and therefore, the cycle time c) is usually set by some market objectives. For more information we refer the interested reader to [5].

2.2 TSALBP-1/3 Formulation According to the TSALBP formulation [2], the 1/3 variant deals with the minimisation of the number of stations, m, and the area ocuppied by those stations, A, in the assembly line configuration. We can mathematically formulate this TSALBP variant as follows:

f 0 (x) = m =

Min

UBm

∑

k=1

f 1 (x) = A =

max x jk ,

j=1,2,...,n

(1)

n

∑ a j x jk k=1,2,...,UBm max

(2)

j=1

subject to: Lj

∑

x jk = 1,

j = 1, 2, ..., n

(3)

k=E j UBm

∑

k=1

max x jk ≤ m

j=1,2,...,n

n

∑ t j x jk ≤ c,

(4)

k = 1, 2, ...,UBm

(5)

k = 1, 2, ...,UBm

(6)

j=1 n

∑ a j x jk ≤ A,

j=1

Adding Diversity to MO Constructive Metaheuristics for the TSALBP Li

∑

k=Ei

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Lj

kxik ≤

∑

kx jk ,

j = 1, 2, ..., n; ∀i ∈ Pj

(7)

k=E j

x jk ∈ {0, 1},

j = 1, 2, ..., n; k = 1, 2, ...,UBm

(8)

where: • n is the number of tasks, • x jk is a decision variable taking value 1 if task j is assigned to station k, and 0 otherwise, • a j is the area information for task j, • UBm is the upper bound for the number of stations m, • E j is the earliest station to which task j may be assigned, • L j is the latest station to which task j may be assigned, • UBm is the upper bound of the number of stations. In our case, it is equal to the number of tasks, and Constraint in equation 3 restricts the assignment of every task to just one station, 4 limits decision variables to the total number of stations, 5 and 6 are concerned with time and area upper bounds, 7 denotes the precedence relationship among tasks, and 8 expresses the binary nature of variables x jk .

2.3 Multiple ant Colony System MACS was proposed as a was proposed as a multiobjective extension of the ant colony system (ACS) [9]. MACS uses a single pheromone trail matrix τ and several heuristic information functions η k (in our case, η 0 for the operation time t j of each task j and η 1 for its area a j ). From now on, we restrict the description of the algorithm to the case of two objectives. In this way, an ant moves from node i to node j by applying the following transition rule: arg max j∈Ω (τi j · [ηi0j ]λ β · [ηi1j ](1−λ )β ), if q ≤ q0 , (9) j= ˆ i, otherwise. where Ω represents the current feasible neighbourhood of the ant, β weights the relative importance of the heuristic information with respect to the pheromone trail, and λ is computed from the ant index h as λ = h/M, with M being the number of ants in the colony, q0 ∈ [0, 1] is an exploitation-exploration parameter, q is a random value in [0, 1], and iˆ is a node selected according to the probability distribution p( j): ⎧ ⎨ τi j ·[ηi0j ]λ β ·[ηi1j ](1−λ )β , if j ∈ Ω , (10) p( j) = ∑u∈Ω τiu ·[ηiu0 ]λ β ·[ηiu1 ](1−λ )β ⎩ 0, otherwise. Every time an ant crosses edge < i, j >, it performs the local pheromone update as follows: τi j = (1 − ρ ) · τi j + ρ · τ0 .

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Initially, τ0 is calculated by taking the average costs, fˆ0 and fˆ1 , of each of the two objective functions, f 0 and f 1 , from a set of heuristic solutions by applying the expression:

τ0 =

1 fˆ0 · fˆ1

(11)

However, the value of τ0 is not fixed during the algorithm run, as usual in ACS, but it undergoes adaptation. At the end of each iteration, every complete solution built by the ants is compared to the Pareto archive PA which was generated till that moment. This is done in order to check if a new solution is a non-dominated one. If so, it is included in the archive and all the dominated solutions are removed. Then, τ0 is calculated by applying equation (11) with the average values of each objective function taken from the current solutions of the Pareto archive. If τ0 > τ0 , being τ0 the initial pheromone value, pheromone trails are reinitialised to the new value τ0 = τ0 . Otherwise, a global update is performed with each solution S of the Pareto set approximation contained in PA applying the following rule on its composing edges < i, j >:

τi j = (1 − ρ ) · τi j +

ρ f 0 (S) · f 1 (S)

(12)

2.4 A MACS Algorithm for the TSALBP-1/3 In this section we describe the customisation made on all the components of the general MACS algorithm scheme to build our solution methodology. 2.4.1

Heuristic Information

MACS works with two different heuristic information values, η 0j and η 1j , each of them associated to one criterion. In our case, η 0j is related with the required operation time for each task and η 1j with the required area:

η 0j =

| Fj | tj · c maxi∈Ω | Fi |

η 1j =

aj | Fj | · UBA maxi∈Ω | Fi |

where UBA is the upper bound for the area (the sum of all tasks’ areas) and Fj is the set of tasks that come after task j. The second term in both formulae represents a ratio between the number of successors of the task j (the cardinality of the successors set Fj ) and the maximum number of successors of any eligible task belonging to the ant’s feasible neighbourhood Ω . Both sources of heuristic information range in [0, 1], with 1 being the most preferable. As usual in the SALBP, tasks having a large value of time (a large duration) and area (occupying a lot of space) are preferred to be firstly allocated in the stations. Apart from area and time information, we have added another information related

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to the number of successors of the task which was already used in [2]. Tasks with a larger number of successors are preferred to be allocated first. Heuristic information is one-dimensional since it is only assigned to tasks. In addition, it can be noticed that heuristic information has static and dynamic components. Tasks’ time t j and area a j are always fixed while the successors rate is changing through the constructive procedure. This is because it is calculated by means of the candidate list of feasible and non-assigned tasks at that moment. 2.4.2

Pheromone Trail and τ0 Calculation

The pheromone trail information has to memorise which tasks are the most appropriate to be assigned to a station. Hence, pheromone has to be associated to a pair (stationk ,task j ), being k = 1, ..., n and j = 1, ..., n. In this way, contrary to heuristic information, our pheromone trail matrix has a bi-dimensional nature since it links tasks with stations. In every ACO algorithm, an initial value for the pheromone trails has to be set up. This value is called τ0 and it is normally obtained from an heuristic algorithm. We have used two station-oriented single-objective greedy algorithms, one per heuristic, to compute it. These algorithms open the first station and select the best possible task according to their heuristic information (related either with the duration time and successors rate η 0j , or the area and successors rate η 1j ). This process is repeated till there is not any task that can be included because of the cycle time limit. Then, a new station must be opened. When no more tasks are to be assigned, the greedy algorithm finishes. τ0 is then computed from the costs of the two solutions obtained by the greedy algorithm using the following MACS equation: τ0 = f 0 (S )·1f 1 (S ) . time

2.4.3

area

Randomised Station Closing Scheme and Transition Rule

Our approach follows a station-oriented procedure, which starts opening a station and selecting the most suitable task to be assigned. When the current station is loaded maximally, it is closed and the next one is opened and ready to be filled. At the beginning, we decided to close the station when it was full in relation to the fixed cycle time c, as usual in SALBP and TSALBP applications. We found that this scheme did not succeed because the obtained Pareto fronts did not have enough diversity. Thus, we introduced a new mechanism in the construction algorithm to close the station according to a probability, given by the filling rate of the station: ∑i∈Sk ti (13) c This probability distribution is updated at each construction step. A random number is uniformly generated in [0, 1] after each update to decide whether the station is closed or not. If the decision is not to close the station, we choose the next task among all the candidate tasks using the MACS transition rule and the procedure goes on. p (closing Sk ) =

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Because of the one-dimensional nature of the heuristic information, the original transition rule (Equation 9) that chooses among all the candidate tasks at each step, has been modified: arg max j∈Ω (τk j · [η 0j ]λ β · [η 1j ](1−λ )β ), if q ≤ q0 , (14) j= ˆ i, otherwise, where iˆ is a node selected by means of the following probability distribution: τk j ·[η 0j ]λ β ·[η 1j ](1−λ )β p( j) = ∑u∈Ω τku ·[ηu0 ]λ β ·[ηu1 ](1−λ )β , if j ∈ Ω , (15) 0, otherwise.

2.5 MORGA Our diversification generation mechanism behaves similarly to a GRASP construction phase [11]. The most important element in this kind of construction is that the selection of the task at each step must be guided by a stochastic greedy function that is adapted with the pseudo-random selections made in the previous steps. We introduce randomness in two processes. On the one hand, allowing each decision to be randomly taken among the best candidates. On the other hand, closing the station according to a probability distribution. We use the same constructive approach, with closing probabilities at each constructive step, than in the MACS algorithm. The probabilistic criterion to select the next task that will be included in the current station is changed to be only based on heuristic information. Therefore, to make a decision among all the current feasible candidate tasks we use a single heuristic value given by:

ηj =

tj aj | Fj | · · c UBA maxi∈Ω | Fi |

(16)

The decision is made randomly among the selected tasks in the restricted candidate list (RCL) by means of the following procedure: we calculate the heuristic value of every feasible candidate task to be assigned to the current open station. Then, we sort them according to their heuristic values and, finally, we set a quality threshold for the heuristic given by q = maxη j −γ · (maxη j − minη j ). All the tasks with a heuristic value η j greater or equal than q are selected to be in the RCL. γ is the diversification-intensification trade-off control parameter. When γ = 1 there is a completely random choice inducing the maximum possible diversification. In contrast, if γ = 0 the choice is close to a pure greedy decision, with a low diversification. As MACS, the MORGA construction algorithm also incorporates a mechanism which allows us to close a station according to a probability distribution, given by the filling rate of the station (see equation (13)).


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3 Using a Multi-colony Approach on the MACS-TSALBP-1/3 and MORGA Algorithms The MACS-based TSALBP-1/3 algorithm proposed in [7] carries the problem of not providing enough intensification in some Pareto front areas, since there is a low probability of filling stations completely. Hence, there is a need to find a better intensification-diversification trade-off. This objective can be achieved by introducing different filling thresholds associated to the ants that build the solution. These thresholds make the different ants in the colony have a different search behaviour. Thus, the ACO algorithm becomes multi-colony [14]. In our case, thresholds are set between 0.2 and 0.9 and they are considered as a preliminary step before deciding to close a station. Therefore, the solution construction procedure is modified. We compute the station closing probability distribution as usual based on the station current filling rate (equation (13)). However, only when the ant’s filling threshold has been overcome, the random decision of either closing a station or not according to that probability distribution is considered. Otherwise, the station will be kept opened. Thus, the higher the ant’s threshold is, the more complete the station will be likely to be. This is due to the fact that there are less possibilities to close it during the construction process. In this way, the ant population will show a highly diverse search behaviour, allowing the algorithm to properly explore the different parts of the optimal Pareto fronts by appropriately spreading the generated solutions. We have also used the same filling thresholds technique for the MORGA. In the MACS algorithm, these filling thresholds are applied in parallel following the multicolony approach. Unlike the MACS algorithm, different thresholds are only used in isolation at each iteration in the case of the MORGA.

4 Experimentation 4.1 Problem Instances and Parameter Values Ten problem instances with different features have been selected for the experimentation: arc111 with cycle time limits of c = 5755 and c = 7520 (P1 and P2), barthol2 (P3), barthold (P4), heskia (P5), lutz2 (P6), lutz3 (P7), mukherje (P8), scholl (P9), and weemag (P10). Originally, these instances were SALBP-1 instances only having time information. However, we have created their area information by reverting the task graph to make them bi-objective (as done in [2])1 . We run each algorithm 10 times with different random seeds, setting the time as stopping criteria (900 seconds). All the algorithms were launched in the same computer: Intel PentiumT M D with two CPUs at 2.80GHz, and CentOS Linux 4.0. 1

Problem instances and more information available at http://www.nissanchair.com/TSALBP

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On the one hand, the values of the parameters used in all the MACS algorithms with and without the new diversification component are as follows. We consider ten different ants, β = 2, and ρ = 0.2. Different values of the transition rule parameter q0 are also studied. In particular: q0 = 0.2, 0.5, 0.8. On the other hand, the MORGA was launched with different diversification-intensification parameter values, γ = {0.1, 0.2, 0.3}. With respect to the parameters of our proposal on using different filling thresholds, there are two ants for each of the five ants’ thresholds considered: {0.2, 0.4, 0.6, 0.7, 0.9} in the MACS algorithm. The same threshold values were used for the MORGA.

4.2 Metrics of Performance We will consider two different multiobjective metrics [8, 17] to evaluate the performance of the two variants of the MACS-based TSALBP-1/3 algorithm and the MORGA. On the one hand, we selected the hypervolume ratio (HVR) from the first group. It can be calculated as follows: HV R =

HV (P) , HV (P∗ )

(17)

where HV (P) and HV (P∗ ) are the volume (S metric value) of the approximate Pareto set and the true Pareto set, respectively. When HV R equals 1, then the approximate Pareto front and the true one are equal. Thus, HV R values lower than 1 indicate a generated Pareto front that is not as good as the true Pareto front. We should notice that the true Pareto fronts are not known in our real-world problem instances. Thus, we will consider a pseudo-optimal Pareto set, i.e. an approximation of the true Pareto set, obtained by merging all the (approximate) Pareto sets Pij generated for each problem instance by all the existing algorithms for the problem in the different runs [5]. Thanks to this pseudo-optimal Pareto set, we can compute HV R and consider it in our analysis of results. On the other hand, we have also considered the binary set coverage metric C to compare the obtained Pareto sets two by two based on the following expression: C(P, Q) =

|{q ∈ Q ; ∃p ∈ P : p ≺ q}| , |Q|

(18)

where p ≺ q indicates that the solution p, belonging to the approximate Pareto set P, dominates the solution q of the approximate Pareto set Q in a minimisation problem. Hence, the value C(P, Q) = 1 means that all the solutions in Q are dominated by or equal to solutions in P. The opposite, C(P, Q) = 0, represents the situation where none of the solutions in Q are covered by the set P. Note that both C(P, Q) and C(Q, P) have to be considered, since C(P, Q) is not necessarily equal to 1 −C(Q, P). We have used boxplots based on the C metric that calculates the dominance degree of the approximate Pareto sets of every pair of algorithms (see Figure 1 and 2).


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Fig. 1 C metric values represented by means of boxplots comparing MACS with and without multi-colony scheme (i.e. variable filling thresholds)

Each rectangle contains ten boxplots representing the distribution of the C values for a certain ordered pair of algorithms in the ten problem instances (P1 to P10). Each box refers to algorithm A in the corresponding row and algorithm B in the corresponding column and gives the fraction of B covered by A (C(A, B)).

4.3 Analysis of Results The experimental results obtained by the two MACS variants with and without the diversity mechanism can be seen in the C metric boxplots of Figure 1 and in the HV Rvalues in Table 1. Some conclusions can be reached from the analysis of the C metric values: • Comparing both versions of MACS, the original one with a specific value of q0 and its counterpart multi-colony extension, we can see that significantly “better”2 results are provided by the latter MACS with thresholds. It happens regardless of 2

When we refer to the best or better performance comparing the C metric values of two algorithms we mean that the Pareto set derived from one algorithm significantly dominates that one achieved by the other. Likewise, the latter algorithm does not dominate the former one to a high degree.

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Table 1 Mean and standard deviation values (in brackets) of the HV R metric for the MACS algorithm. In each problem instance, the best mean value is in bold. A1: MACS 0.2 (without thr.), A2: MACS 0.5 (without thr.), A3: MACS 0.8 (without thr.) A4: MACS 0.2 (with thr.), A5: MACS 0.5 (with thr.), A6: MACS 0.8 (with thr.)

P1

P2

P3

P4

P5

A1 A2 A3 A4 A5 A6

0.5532 (0.023) 0.5549 (0.019) 0.5331 (0.008) 0.9051 (0.01) 0.8770 (0.009) 0.8353 (0.008) P6

0.6655 (0.009) 0.6600 (0.017) 0.6418 (0.014) 0.8962 (0.013) 0.8839 (0.016) 0.8522 (0.010) P7

0.6418 (0.026) 0.6331 (0.012) 0.6172 (0.016) 0.8852 (0.020) 0.8617 (0.016) 0.8285 (0.022) P8

0.4297 (0.043) 0.4475 (0.034) 0.4629 (0.061) 0.8176 (0.027) 0.7969 (0.024) 0.8191 (0.018) P9

0.9686 (0.006) 0.9660 (0.006) 0.9608 (0.007) 0.8695 (0.022) 0.8471 (0.013) 0.8114 (0.018) P10

A1 A2 A3 A4 A5 A6

0.6729 (0.022) 0.6833 (0.036) 0.6486 (0.036) 0.8430 (0.022) 0.8368 (0.016) 0.7284 (0.054)

0.8222 (0.315) 0.7101 (0.246) 0.6523 (0.239) 0.9723 (0.066) 0.8812 (0.058) 0.7330 (0.066)

0.5522 (0.019) 0.5480 (0.013) 0.5365 (0.019) 0.8979 (0.011) 0.8988 (0.013) 0.8656 (0.011)

0.6014 (0.017) 0.5968 (0.015) 0.6070 (0.019) 0.8941 (0.011) 0.8829 (0.012) 0.8506 (0.013)

0.7830 (0.019) 0.7819 (0.035) 0.7789 (0.014) 0.7674 (0.028) 0.7535 (0.037) 0.7067 (0.052)

Table 2 Mean and standard deviation values (in brackets) of the HV R metric for the MORGA. In each problem instance, the best mean value is in bold. A1: MORGA 0.1 (without thr.), A2: MORGA 0.2 (without thr.), A3: MORGA 0.3 (without thr.) A4: MORGA 0.1 (with thr.), A5: MORGA 0.2 (with thr.), A6: MORGA 0.3 (with thr.)

P1

P2

P3

P4

P5

A1 A2 A3 A4 A5 A6

0.5792 (0.012) 0.5779 (0.012) 0.5624 (0.026) 0.9258 (0.005) 0.9333 (0.007) 0.9542 (0.007) P6

0.6602 (0.018) 0.6550 (0.008) 0.6789 (0.017) 0.9093 (0.005) 0.9121 (0.005) 0.9385 (0.007) P7

0.6017 (0.023) 0.6294 (0.042) 0.6028 (0.019) 0.7560 (0.005) 0.6528 (0.008) 0.6488 (0.009) P8

0.4278 (0.04) 0.3957 (0.035) 0.4129 (0.017) 0.8457 (0.020) 0.9262 (0.019) 0.9366 (0.016) P9

0.9137 (0.007) 0.9294 (0.010) 0.9302 (0.009) 0.8642 (0.007) 0.8953 (0.038) 0.9149 (0.052) P10

A1 A2 A3 A4 A5 A6

0.5784 (0.020) 0.5909 (0.029) 0.6451 (0.043) 0.7611 (0.029) 0.8361 (0.033) 0.8847 (0.038)

0.6914 (0.223) 0.5447 (0.09) 0.6730 (0.237) 0.7034 (0.260) 0.7498 (0.039) 0.7466 (0.067)

0.5176 (0.015) 0.5316 (0.022) 0.5301 (0.026) 0.8769 (0.009) 0.8797 (0.008) 0.9011 (0.006)

0.5861 (0.012) 0.5807 (0.016) 0.5873 (0.017) 0.8606 (0.004) 0.8663 (0.004) 0.8610 (0.007)

0.7911 (0.026) 0.7939 (0.027) 0.7994 (0.031) 0.8568 (0.018) 0.8726 (0.017) 0.8837 (0.022)


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Fig. 2 C metric values represented by means of boxplots comparing the MORGA with and without using the variable filling thresholds

the value of q0 , and it is common in all the problem instances but P5 (heskia). This is because of the nature of that problem instance, whose pseudo-optimal Pareto front is not wide enough. Every solution of this problem instance is found in the central part of the objective space, so the diversity introduced by the filling thresholds is not useful. • We find less performance differences with a lower value of q0 . It makes sense since MACS with higher q0 values gives more importance to a higher intensification in the selection procedure and thus, the Pareto fronts are more similar. Hence, the algorithm does not take advantage of the diversity induced by the thresholds approach. • If we compare every MACS variant with and without thresholds, regardless of the value of q0 , the conclusion is that MACS 0.2 with thresholds is the best approach. It gets better results than MACS 0.5 and 0.8 with thresholds in every problem instance. It is only dominated by MACS 0.2 and 0.5 without thresholds in P5. Even in a non-common problem instance like P5, results are good enough. Hence, the diversity of the task selection procedure (a low value of q0 parameter) and the use of variable station filling thresholds are both important to solve the problem appropriately. Nevertheless, if we select MACS 0.8 with thresholds and MACS without thresholds with lower values of q0 (0.2 and 0.5) to be compared,

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Fig. 3 Pareto fronts of the MACS algorithm and MORGA for the P3 and P10 problem instances respectively

we can notice that the former algorithm outperforms the latter two in five and six problem instances respectively. On the contrary, the latter two are better in four of them. All of these algorithms have thus quite similar results. Consequently, the variable filling thresholds in isolation are not enough to get a good yield. There is also a demand for diversity in the randomised task selection procedure of the algorithm which requires a good diversification-intensification trade-off. On the other hand, we show the results of the MORGA with and without the diversity mechanism. In Figure 2, the boxplots of the C metric are shown. Similar conclusions can be obtained: • The MORGA variants with the diversity mechanism almost always achieve better performance than those without it. • Only in the P5 instance, there are solutions of the MORGA variants with the diversity mechanism which are dominated by the algorithms without the new approach.


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• It is clear how the MORGA with γ = 0.3 is the best of the MORGA variants, and its version with the diversity mechanism the best algorithm. In general terms, we can draw similar conclusions analysing the HV R metric values (see Tables 1 and 2). They are always higher in variants with thresholds as they better converge towards the true (i.e., pseudo-optimal) Pareto fronts. For example, that is shown in the Pareto fronts of Figure 3 that graphically shows the aggregated Pareto fronts corresponding to P3 and P10 instances for the MACS algorithm and MORGA.

5 Concluding Remarks In a previous contribution [7] we demonstrated that the use of multiobjective constructive metaheuristics to tackle the TSALBP-1/3, particularly a MACS algorithm, was a good choice. And the consideration of a stochastic procedure to decide when to close a station performed better choice than a pure station-based approach. Nevertheless, that solution still leads to situations where intensification was too high in a specific region of the Pareto front. That is an undesirable situation for the plant managers who should be provided with all the configurations of their contextual interest in the objective space. To solve this problem, in this contribution we showed a better intensificationdiversification trade-off. It could be achieved in a MOACO algorithm by introducing different filling thresholds associated to the ants that build the solution in order to provide a different search behaviour to the different ants in the colony. We also applied a modified version of this new diversity mechanism to a multiobjective randomised greedy algorithm (MORGA). Ten well-known problem instances of the literature were selected to test our proposal. From the obtained results we have found out that the best yield to globally solve the problem belongs to the new MACS-TSALBP-1/3 algorithm using the multi-colony scheme with q0 = 0.2. Likewise, the MORGA with additional diversity clearly outperforms the results of the basic one. In the future we aim to consider other multiobjective constructive metaheuristics and apply a local search to increase the current performance. Acknowledgements. This work is supported by the UPC Nissan Chair and the Spanish Ministerio de Educación y Ciencia under project DPI2007-63026 and by the Spanish Ministerio de Ciencia e Innovación under project TIN2009-07727, both including EDRF fundings.

References 1. Barán, B., Schaerer, M.: A multiobjective ant colony system for vehicle routing problem with time windows. In: 21st IASTED Conference, Innsbruck Germany, pp. 97–102 (2003) 2. Bautista, J., Pereira, J.: Ant algorithms for a time and space constrained assembly line balancing problem. European Journal of Operational Research 177, 2016–2032 (2007)

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3. Baybars, I.: A survey of exact algorithms for the simple assembly line balancing problem. Management Science 32(8), 909–932 (1986) 4. Chankong, V., Haimes, Y.Y.: Multiobjective Decision Making Theory and Methodology. North-Holland, Amsterdam (1983) 5. Chica, M., Cordón, O., Damas, S., Bautista, J.: Multi-objective, constructive heuristics for the 1/3 variant of the time and space assembly line balancing problem: ACO and randomised greedy. Tech. Rep. AFE-09-01, European Centre for Soft Computing, Asturias (Spain) (submitted to Information Sciences) (2009) 6. Chica, M., Cordón, O., Damas, S., Bautista, J.: A multiobjective GRASP for the 1/3 variant of the time and space assembly line balancing problem. In: 23rd International Conference on Industrial, Engineering & Other Applications of Applied Intelligent Systems (IEA-AIE 2010), Cordoba, Spain (to appear, 2010) 7. Chica, M., Cordón, O., Damas, S., Bautista, J., Pereira, J.: A multiobjective ant colony optimization algorithm for the 1/3 variant of the time and space assembly line balancing problem. In: 12th International Conference on Processing and Management of Uncertainty in Knowledge-based Systems (IPMU), Málaga (Spain), pp. 1454–1461 (2008) 8. Coello, C.A., Lamont, G.B., Van Veldhuizen, D.A.: Evolutionary Algorithms for Solving Multi-objective Problems, 2nd edn. Springer, Heidelberg (2007) 9. Dorigo, M., Gambardella, L.: Ant colony system: a cooperative learning approach to the traveling salesman problem. IEEE Transactions on Evolutionary Computation 1(1), 53–66 (1997) 10. Dorigo, M., Stützle, T.: Ant Colony Optimization. MIT Press, Cambridge (2004) 11. Feo, T.A., Resende, M.G.C.: Greedy randomized adaptive search procedures. Journal of Global Optimization 6, 109–133 (1995) 12. Garc´ıa Mart´ınez, C., Cordón, O., Herrera, F.: A taxonomy and an empirical analysis of multiple objective ant colony optimization algorithms for the bi-criteria TSP. European Journal of Operational Research 180, 116–148 (2007) 13. Glover, F., Kochenberger, G.A. (eds.): Handbook of Metaheuristics. Kluwer Academic, Dordrecht (2003) 14. Middendorf, M., Reischle, F., Schmeck, H.: Multi colony ant algorithms. Journal of Heuristics 8(3), 305–320 (2002) 15. Scholl, A.: Balancing and Sequencing of Assembly Lines, 2nd edn. Physica-Verlag, Heidelberg (1999) 16. Scholl, A., Becker, C.: State-of-the-art exact and heuristic solution procedures for simple assembly line balancing. European Journal of Operational Research 168(3), 666–693 (2006) 17. Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C.M., Grunert da Fonseca, V.: Performance assessment of multiobjective optimizers: an analysis and review. IEEE Transactions on Evolutionary Computation 7(2), 117–132 (2003)

Construction and Application of a Digital Factory for Automotive Paint Shops Yang Ho Park, Eon Lee, Seon Hwa Jeong, Gun Yeon Kim, Sang Do Noh, Cheol-woong Hwang, Sangil Youn, Hyeonnam Kim, and Hyunshik Shin*

Abstract. To ensure competitiveness in today’s automotive market, growing emphasis is being laid on the collaboration of disparate engineering activities in manufacturing in the automotive industry. By applying virtual manufacturing, diverse engineering activities such as design evaluation, process & material planning, production flow analysis, and ergonomic analysis can be brought together to be performed in a single integrated model, viz., a digital factory. In this paper, we have suggested a procedure, consideration and expected effects for paint shop of automotive company. Therefore, we constructed a digital factory for a paint shop for an automotive company. By applying the digital factory to manufacturing engineering, it is expected that time and cost savings can be realized in many manufacturing engineering work in planning and new product development processes.

1 Introduction In recent years, manufacturers are under tremendous pressure to improve their responsiveness and efficiency in terms of product development, manufacturing preparation, planning, operations, and resource utilization along with transparency in production and quality control. Also, the time and cost for product development and production must be cut as much as possible to meet the changing demands of customers in different regions of the world. Therefore, most manufacturing companies need a new production paradigm that can achieve both competitiveness and fast production. Virtual manufacturing is an integrated computer model that represents the physical (characteristics), logical schema, and behavior of a real manufacturing Yang Ho Park . Eon Lee . Seon Hwa Jeong . Gun Yeon Kim . Sang Do Noh Department of Systems Management Engineering, Sungkyunkwan University, Korea *

Cheol-woong Hwang . Sangil Youn . Hyeonnam Kim . Hyunshik Shin Manufacturing Engineering Center, GM Daewoo Auto&Technology, Korea

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system. It provides the manufacturing engineering content and solutions to create, evaluate, monitor, and control for distributed agile manufacturing based on 3-D CAD, simulation, databases, and computer networks. Generally, virtual manufacturing can verify and optimize many decisions, plans, and operations in manufacturing engineering such as product design, equipment, jig, and fixture design, process planning, factory layout design, production and material flow analysis, and OLP (Off-Line Programming) for various equipment. As a result, it saves time and cost in product development and production [1, 2]. The General Motor corporation has a plan to apply virtual manufacturing technology to their manufacturing systems as part of a math-based manufacturing program that began in 1990. This program means that “every engineer necessitates implementing the manufacturing, assembly system creation, verification, design and operation by using a mathbased model before making prototypes,” [3]. In particular, many reports have investigated the effect of applying virtual manufacturing technology to automotive companies in application deployment and the strategic analysis of virtual manufacturing technology for an overall business process [4]. Using virtual manufacturing technologies, many activities in manufacturing can be integrated and realized into one system, and thus manufacturing cost and the time-to-market can be reduced and productivity can be improved dramatically. According to current reports on virtual manufacturing, the time and cost for making jigs and fixtures have been reduced by more than 75% in aerospace industries, errors in the design of molds and dies have decreased by about 50% in machine shops, and the total development time of production lines has been trimmed by more than 20% in the automotive sector [5]. Fig. 1 shows concepts and structure of virtual manufacturing.

Fig. 1 The concept and structure of a virtual manufacturing [6]

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In this research, we suggest a systematic and effective method for constructing a digital factory of a paint shop. Based on the method, we have constructed a sophisticated digital factory of an automotive paint shop. A real case study in the automotive industry and the effects of virtual manufacturing are presented. This paper aims to build a digital factory of a paint shop in an automotive company more systematically and effectively by analyzing the manufacturing process.

2 Digital Factories A digital factory is an integrated computer model that consists of models of products, machines, human workers, manufacturing processes, jobs, workstations and plants, and it could be a critical base of providing environments for applying virtual manufacturing technology to manufacturing activities that arise in the factory. A digital factory also includes processes, as classified by the range of application of the model and the levels of detail and related information [7]. The use of a digital factory makes it possible to execute a range of activities such as the design of machines, utilities, and tools, the planning of processes and schedules, decisions regarding the factory layout and cells, the establishment of logistics and the assignment of the storage area, OLP performance of production machines, decisions regarding assembly procedures and methods, worker education, task error prevention and improvement, collision checks, and so on; it can also reduce the production time and cost. A digital factory can be used as not only a virtual model of a real factory but also the central control for system audits, control, and decision-making. A digital factory is an integrated environment that is applied across all fields of production. If a digital plant is built and utilized, rapid verification of the production possibility in management processes and new idea development in product development can be possible. Also, product visualization, performance analysis, virtual examination through the production of a virtual prototype, and evaluation of the efficiency and ease of production can be possible in product design. In product manufacturing, the specification of manufacturing utilities, optimization of processes and utilities arrangement, productivity improvement, and cost reduction are possible [8].

3 Automotive Paint Shop and Workflow Analysis There are many engineering activities in developing a new car from “planning” to “start of production.” Fig. 2 shows the general car development process. The development process consists of 'planning,' 'development of the platform,’ 'styling,' 'prototype drawings,' 'prototype building' and 'production drawings,' 'product and process evaluation for a tryout and vehicle match,' 'pilot production,' and 'mass production'. Diverse engineering activities are performed concurrently in each process. A typical paint shop will consist of several painting processes. In rough order, these processes include the electro-coating, sealing, main color painting, inspection, and painting operations. The paint shop processes are such that many of the

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Fig. 2 General product development process in automotive company

operations can be performed without stopping the vehicle at a station. Therefore, the capability and reliability of material handling equipment is important in a paint shop [9]. Fig. 3 shows the typical manufacturing process of an automotive paint shop. The layout of the paint shop in this paper has been composed of three floors: the under, base, and top floors. The under coating, base coating, and top coating processes are conducted at each floor. In terms of storage, the paint shop has Colored Painted Storage (CBS) and Painted Body Storage (PBS). PBS and CBS are buffers in the processes. Especially the PBS area is for temporary storage, before the painted body is transferred to the final assembly line.

Fig. 3 Typical manufacturing process of automotive paint shop


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The manufacturing process of paint shop in this paper is composed mainly of five sub-processes: pretreatment, electro deposition, sealing and under coating, base coat, and top coat. At the stage of pretreatment, the purpose is the elimination of pollutants on the body to increase the quality of painting. Electrodeposition is the first coating on the car body using electronic plating. Sealing and under coating refers to finishing the joint of steel sheet or edge to prevent damage during movement. The next process is base coating. It is the second coating for improving painting. The top-coat process is the third coating for making the final color. Lastly, inspection and modification are performed in an automotive paint shop. In this process, various machines and equipment are required, such as robots and overhead and ground conveyors. As described above, because of continuous and automatic processes in the paint shop, the layout of robots and the conveyor car body is more important. But manual work, as well as automatic lines, exists in current paint shops for inspection and sealing, under coating, masking & sanding, wax coating, minor repair, and heavy repair. Because it is difficult to apply robots or other machines and equipment to these processes, these processes are performed manually. Fig. 4 shows the production flow of an automotive paint shop. Based on these workflow analyses, we analyzed the areas and engineering activities for the application of virtual manufacturing. Table 1 shows the areas, effects, and needed data pertaining to virtual manufacturing for paint shops.

Fig. 4 Production flow of an automotive paint shop

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Table 1 Appilcation of Virtual Manufacturing in Paint Shop

Area Evaluation of drawing Evaluation of equipments for MH Evaluation of interferences Evaluation of quality of painting Design and evaluation of hanger/skid Evaluation of jigs/fixtures Evaluation of layout of operators Evaluation of equipments Training operators

Effects

Data

Design and operation of plant Virtual engineering, verification of process Design and operation of plant Inspection/quality control

P/PR/R P/R

Virtual engineering, verification of process Virtual engineering, verification of process Verification of process

P/PR/R

Design and operation of plant Visualization of product, process, resource

P/R P/PR/R

P/R P/PR/R

P/PR/R P/R

* P: product, PR: process, R: resource

4 Construction of a Digital Factory for a Paint Shop 4.1 Procedure of the Digital Factory To construct a digital factory, 3D CAD and a simulation model must be implemented. Both modeling activities entail considerable time, cost, and effort. Hence, technological developments are essential for effective measurement and geometric modeling, knowledge-based CAD and simulation, and reusable models. In addition to these technologies, systematic planning and decisions regarding the detailed scope and model maintenance are also very important. Because the construction of a digital factory entails a lot of time and cost, first of all, the definition of the purpose and the construction of a detailed and quantified utilization plan are necessary. Therefore, we consider the level of detail and abstraction of the model depending on the purpose and scope of digital factory construction. After the virtual technology is applied, it is necessary to analyze and verify the effects of the result. A step-by-step strategy is important to apply these technologies in practice. Fig. 5 shows the general procedure of digital factory construction.

4.2 Objectives of a Digital Factory In the case of an automotive paint shop, there are so many robots, jigs, and fixtures. Moreover, painting processes are performed in a paint booth, which is a closed area with harmful objects, such as paints, thinners, etc. Therefore, it is not


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Fig. 5 General procedures to digital factory construction

easy to evaluate machines and equipment in a real work environment. Because of the harmful and closed work environment in a painting shop, a digital factory is required for evaluating various engineering activities. The objectives of a digital factory for automotive companies are listed below. • Planning of the construction and operation of a new plant for new car development • Evaluation of the design data at the early design stage • Evaluation of new machines and equipment, especially interference checks among jigs, fixtures, products, facilities, and robots • Evaluation of new processes during new car production

4.3 Construction of a Digital Factory for a Paint Shop Paint processes consist of detailed handling processes in a real automotive paint shop. These processes are conducted in a paint booth with chemicals. These processes are continuously performed via conveyors, hangers, or carriers; hence, the paint process has a longest production line in the automotive production line. Hence, the carrier/hanger size and conveyor location, besides the paint booth size, are important parameters in a paint shop. In this research, we constructed a digital factory of a paint shop using the proposed construction method, objectives, and considerations. Figs. 6 to 9 show the constructed digital factory for an automotive paint shop. The digital factory of the paint shop constructed in this paper is illustrated in Fig. 6, and Fig. 7 shows the PBS (Paint Body Storage) area in the shop.

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Fig. 6 The digital factory of paint shop

Fig. 7 Painted body storage (PBS) area

Fig. 8 shows an example of overhead and skid conveyors for the transfer of the car body frame along the process line in the paint shop. And Fig. 9 shows the pretreatment process line that is composed of a paint booth and a skid conveyor.


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Fig. 8 Overhead and skid conveyors

Fig. 9 Sealing and under coat line

5 Results of Application We developed an arrangement of machines and equipment, such as the conveyor and the paint booth, followed by a check of interference between facilities and an advance evaluation of the car design data by integrating the 3-dimensional CAD model of the constructed paint digital factory, which included robots, construction

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parts, and facilities. Fig. 10 shows a case of applying the constructed digital paint shop model to the areal analysis of manual workstations in the paint shop pertaining to inspection, heavy repair, etc.

Fig. 10 Evaluation of workstation in paint shop

Interference checking was possible across the frame/booth and conveyor/facility, as shown in Figs. 11 and 12. Figs. 13 depict examples of design and process changes in plant facilities. Hence, it is possible to evaluate the arrangement and size of plant facilities in a virtual environment.

Fig. 11 Interference check between booth and conveyor in Pretreatment line


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Fig. 12 Interference check between booth and conveyor in base coat

Fig. 13 Modification of skid design and skid conveyor arrangement

6 Conclusions In this paper, we have suggested systematic methods, considerations, and expectations as the core basis for applying virtual manufacturing technologies to the engineering activities of an automotive paint shop in new car development. By applying a systematic and efficient method in 3D modeling, the construction of a digital paint shop is more systematic and efficiently performed. Using the digital

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factory of a paint shop, we evaluated the plant layout and the processes. Moreover, we conducted various engineering activities efficiently in practical fields on a virtual-manufacturing basis. By continuous verification using virtual manufacturing technologies, savings in time and cost for many manufacturing preparation activities in new car development processes are enabled in automotive companies. An extended study based on the proposed methodologies in virtual manufacturing is necessary for the entire process of new car development. Acknowledgement. This research was supported by the Brain Korea 21 project sponsored by the Korean Research Foundation. This support is gratefully acknowledged.

References [1] Noh, S.D., Lee, C.H., Hahn, H.S.: Virtual Manufacturing for an Automotive Company(II) - Construction and Operation of a Virtual Body Shop. IE Interfaces 14(2), 127–133 (2001) [2] Noh, S.D., Park, Y.-J.: Manufacturing Preparations in the New Car Development for an Automotive Body Shop by Digital Manufacturing Technologies. Transaction of KSAE 11(6), 118–126 (2003) [3] Lee, J.H.: New product development process of digital manufacturing role and present condition. Mechanical Journal 41(10) (2001) [4] Noh, S.D., Lee, C.H., Hahn, H.S.: Virtual Manufacturing for an Auto-motive Company(I) - Workflow Analysis and Strategic Planning of Manufacturing Prepara-tion Activities Construction and Operation of a Virtual Body Shop. IE Interfaces 14(2), 120–126 (2001) [5] Brown Associates, D.H. Inc., Providing its Worth: Digital Manufacturing’s ROI (1999) http://www.bara.org.uk/info/digital/Digital_Manufacturing_ ROI.pdf (Accessed February 18, 2010) [6] Noh, S.D., Lee, K.I., Han, H.S., Park, Y.-j., Shin, H.-s., Chung, K.H.: Using Virtual Manufacturing Technologies for Continuous Verification of Products, Processes and Resources in the Manufacturing Preparation of Automotive Companies. In: The 35th CIRP-Insternational Seminar on Manufacturing Systems, vol. 12(15), pp. 245–252 (2002) [7] Iwata, K., Onosato, M., Teranoto, K., Osaki, S.: A modeling and simulation Architecture for Virtual Manufacturing Systems. Annals of the CIRP 44(1), 379–383 (1995) [8] Lee, K.I., Noh, S.D.: Virtual Manufacturing System - a Test-bed of Engineering Activities. Annals of the CIRP 46(1), 347–350 (1997) [9] Ulgen, O., Gunal, A.: Handbook of Simulation. John Wiley & Sons, Inc., The United States of America (1998)

Resource Efficiency in Bodywork Parts Production Reimund Neugebauer and Andreas Sterzing*

Abstract. The need for even greater efficiency in handling resources is coming to be seen as a public duty in politics, commerce and research. At the same time this raises the question of what options are open to companies in the manufacturing industries - and, in particular, the OEMs and suppliers to the automotive industry for reducing costs as well as deployment of resources and emissions. In addition to illustrating and analysing the relevance of this topic as far as forming technology is concerned, the following article discusses a selection of approaches that are being adopted in the Fraunhofer Institute for Machine Tools and Forming Technology with a view to reducing the consumption of resources, particularly in the bodywork parts production sector.

1 Background The 21st century is pushing humanity closer to its pre-ordained limits. Whilst the population of the Earth is increasing, the availability of raw materials for industrial enterprises as well as for developing countries is diminishing. Consumerism in developing countries such as China and India, orientated as it is towards the more prosperous nations, calls for a massive increase in gross national product worldwide. As a result, we can expect competition on a global scale for those resources that remain. One aspect that is playing a significant role in this global development and drastically intensifying this situation is humanity’s growing need for mobility. Whereas today some 72 million motor vehicles are produced worldwide, it may be assumed that this figure is poised to increase dramatically over the next few years. Reimund Neugebauer . Andreas Sterzing Fraunhofer Institute for Machine Tools and Forming Technology IWU Reichenhainer Strasse 88 09126 Chemnitz, Germany e-mail: [email protected], [email protected] *

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Hence the need emerges to reduce the quantity of resources consumed at the same time as increasing product output and so to enhance resource productivity. That is, to manufacture as much as possible using a defined quantity of raw materials and energy. The challenge is, therefore, to bring about a drastic reduction in the consumption of resources at the same time as a conspicuous increase in economic growth. The pre-condition for this is technological innovation and longterm investment. Companies that work hard today to give themselves a cost advantage based on efficiency technologies will find themselves in a better position to extend this competitive edge in the future.

2 Relevance for the Manufacture of Bodywork Components Using Forming Techniques The fact that the cost of resources – and in particular the cost of energy – has in most cases previously played only a subordinate role in investment-related decisions is demonstrated by the results of a survey conducted among company decision-makers as part of an EFFPRO (Energy Efficiency in Production) [2] study sponsored by the Federal Institute for Education, Science, Research and Technology (BMBF). More than half of those questioned indicated that these costs had either no effect at all on their scheduled investments or only affected them to a minor extent. In addition, only one third of the companies had even basic facilities at their disposal for assessing resource/energy efficiency or for optimising production processes. However, the dynamic upward trend of prices which has been a feature of the last few years in regard to raw materials and energy is likely to be sustained. Global problems such as overall competition for resources, statutory emissions limits and demographic effects will determine individual company scenarios. Resource/energy efficiency will, in the future, no longer be a matter of merely protecting the environment but primarily a question of operating efficiency. The use of efficiency technologies will thus come to represent a significant pre-requisite for the success of any enterprise in the marketplace and, ultimately, lead to sustained competitive advantages. In motor vehicle production, bodywork represents the component assembly with the greatest cumulative energy expenditure KEAH (Fig. 1). In addition to the supply of the primary materials, other aspects reflected in cumulative energy expenditure include the fabrication of the forming tools and implementation of the actual forming processes. The Fraunhofer Institute for Machine Tools and Forming Technology has set itself the following challenge: by means of innovative solutions, to make a contribution towards reducing the consumption of resources and energy in bodywork manufacture. In addition to the consistent implementation of lightweight construction strategies, a factor which also has a positive effect on the subsequent fuel

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consumption of the vehicles, the development of flexible, re-configurable forming tools as well as the application of resource-saving manufacturing technologies and facilities represents a promising approach.

Fig. 1 Cumulative energy expenditure (KEAH) in relation to the overall vehicle [1]

3 The Need for Action – Augmenting Resource Efficiency in Bodywork Manufacture The conclusions to the above study also included fields of operation as defined by the companies participating in the survey to enable a significant reduction in the resources and energy deployed in the manufacture of bodywork parts. To ensure that positive effects are achieved relatively quickly (i.e. within the next two years), the optimization of individual stages in the process within existing process chains is being viewed as a promising measure. The substitution of individual stages in the process with innovative, resource-saving technologies was identified as a medium-term approach which, it is felt, should produce successes within 2 to 5 years. By way of further measures to increase efficiency, the elimination of complete stages in the process and their replacement with new construction methods as well as resource-saving technology, tooling and system concepts have been specified with a view to achieving shorter process chains. Because the greatest challenges lie in guaranteeing appropriate process capability and stability, implementation and usage in production is only envisaged after a period of 5 years. These solutions will only be implemented if the associated risks as far as the company is concerned can be kept under control. This calls for innovations which, in addition to a high level of resource and energy efficiency, also demonstrate corresponding suitability for volume production as well as a high level of process and application capability. Because under no circumstances must the implementation of these technologies and process chains be allowed to result in shutdowns and consequential loss of production. This forms the basis for further research to be conducted over the next few years. In the following, therefore, examples will be presented showing how, by applying efficiency technologies and facilities, a definite increase in resource and energy efficiency can be achieved in the manufacture of bodywork components based on forming techniques, but at the same time emphasising that consideration must always be given to the process chain as a whole.

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4 Technological Applications 4.1 Material Characterization/Characteristics Determination One important strategy for increasing resource efficiency is to identify and compensate for possible errors at the very beginning of the product development process. This means that careful preparation in relation to the process is more important than ever. Hence the use of FE simulation for designing forming processes acquires a strategic role. However, in order to be able to use simulation as an effective tool, precision results are required which in turn call for precise input values and suitable material models to describe the forming behaviour. A systematic expansion of the characteristics determination process (Fig. 2), a more precise calculation of the flow curves and yield loci, linked with new materials test methods such as, for example, the Maxi-BulgeTest or accurate determination of the start of flow in the tension compression test with high-resolution temperature measurement will lead to a reduction of iteration loops in the simulation and to a significant improvement in the accuracy of simulation calculations. This in turn will have a positive effect on the real tryout process because here too it will be possible to reduce the number of iteration loops. In the bodywork component fabrication sector, temperature-assisted forming processes are gaining more and more importance. So-called ’form hardening’ represents the state of the art and is already being used for a broad spectrum of components. The use of temperature as a process parameter in the processing of magnesium and aluminium alloys using forming technology also provides us with the opportunity of extending the area of application for these materials and thus to make a contribution towards reducing component weights. Here too FE simulations are essential for the design and layout of such processes and, by comparison to traditional sheet metal forming at room temperature, represent the emergence of a new quality factor. Phenomena that may also occur at room temperature but which do not actually have any effect on the forming result as far as the accuracies normally demanded are concerned may be of major significance here. Aspects such as, for example, • • • • • •

flow curves dependent on temperature and expansion rate, temperature- and load-dependent heat transfer coefficients, temperature-dependent heat capacity and heat conductivity capacity, modelling of micro-structural transformations, volume changes in relation to micro-structural transformations and temperature-dependent failure limits of the material

must be taken into account. There is a need for further action in relation to the determination, provision and observance of these temperature-specific input parameters.


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IWU strategy „material testing“ uniaxial tensile test Maxi-BulgeTest

τσΙΙ

II

ϑmax = 1200 °C

τσΙI

tensile-compression test

yield locus diagram

biaxial tensile test

Fig. 2 IWU strategy “extending characteristics determination” [7]

4.2 Efficiency Technologies 4.2.1 Process Monitoring Reducing scrap and avoiding re-working is an important point of departure in optimising the use of energy and resources in bodywork parts manufacture. The current status is characterised by the fact that the quality test is carried out at the end of a press line. Because of the necessary forming and trimming steps it is possible that, when a fault is determined (e.g. necking, cracks), a number of parts may already be affected. One approach that is being used at IWU Chemnitz is the development of suitable process monitoring strategies that enable a rapid response to be made to changes in process conditions. One challenge lies in the identification of appropriate variables that characterise the status of the process. A possible method for identifying appropriate information about the process is by registering the flange movement, which is influenced by a large number of factors. In so doing (and without the need for precise know-ledge of these factors) open or closed loop control techniques as applicable may be deployed in relation to the flange movement by changing the blank holder force [4, 6, 11]. By specifying the process limits for the manufacture of good parts and by logging the trend of progression of the movement of the metal sheet, it is possible to adjust the blank holder force at an early stage should the corresponding tolerance limits be exceeded and hence to significantly reduce the amount of scrap (Fig. 3).

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This strategy has already been used under production conditions using actual components as a model. Taking a longitudinal beam as an example, it proved possible to reduce the scrap rate from 12 % to less than 2 %.

Gutte

Teil part

3200 kN

3400 kN 3600 kN

blankholder force settings Einstellungen Kissenkraft F N FBH [kN]

3200 kN

3000 kN

aus Erf

3400 kN

measuring measuring of flange flange movement

good parts

flange movement ss [mm] Flanscheinzug [mm]

Palette change Cushion force change Flange movement Test part

Fig. 3 Online process monitoring based on flange movement

4.2.2 Use of High-Speed Cutting Processes Depending on the actual forming process, the fabrication of bodywork components using forming technology frequently calls for additional cutting and/or punching operations prior to producing the final component geometry. One of the operations included here is the trimming of formed parts. Another operation is the introduction of perforations or form contours into the component so as to guarantee further processing capability as well as the function of the component. Because of the increasing importance of lightweight materials and, in particular, the growing use of high- and super-strength materials, conventional cutting processes are fast approaching their limits as far as the necessary process forces, achievable quality and realistic service life are concerned. This is leading to the use of laser cutting, e.g. for trimming form-hardened components. In addition to the thermal impact on the material, this approach does not represent an optimum solution from an energy point of view either. Adiabatic separation, as it is known, a technique that has been previously used in particular for separating small diameter cylindrical solid profiles, offers an opportunity to replace laser cutting in the ’form hardening’ process chain, thus achieving a positive influence on the overall energy balance in component manufacture [5, 8]. In addition, the process offers the potential to avoid the need for any re-working because the cut surfaces are produced to a very high quality and are practically burr-free. It is possible, when manufacturing tube-shaped structural components, for this process to replace corresponding sawing operations previously used to provide semi-finished goods and/or for finish machining of the components. In addition to high cut section quality, it is also possible to achieve a considerable increase in the level of material utilization because no chips are produced.


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Thus, based on an in-depth scientific analysis of adiabatic separation, the technical pre-conditions and fundamentals for expanding the field of application of adiabatic separation to bodywork parts manufacture are being created (Fig. 4) at Fraunhofer IWU with a view to providing a framework within which the relevant mechanisms and factors likely to affect the separation result can be identified and evaluated. Resource Efficiency by Innovative Forming/Cutting Processes Ö

adiabatic cutting

vcut Fcut

vcut Fcut

α1

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- effects - limits - tool/process design

Di Da

α2 vcut Fcut

test tube (1.0037; D = 60 mm, s0 = 2,0 mm)

OBJECTIVE application extension Ö Ö

α2

α1

Limited know-how HSIC

cutting / punching of tubes trimming / punching of flat sheet parts

test sheet part (1.0335, s 0 = 5,0 mm)

Fig. 4 Expansion of the application field for adiabatic separation processes

4.2.3 Shortening the Process Chain by Combining Processes The development of forming strategies for the flexible manufacture of component derivatives also represents one approach to increasing the efficiency of resource deployment in bodywork manufacture. Further successes here may be achieved by the use of a universal blank to serve as a basis for the subsequent production of the derivatives (Fig.5).

Fig. 5 Universal perform

As part of a joint project with various industrial enterprises led by BMW AG the fundamental feasibility of this approach was examined and substantiated, taking a drive console as an example [3, 8]. A traditional deep drawing operation was

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used in the creation of the universal blank. The console derivatives (drive console left, drive console 4-wheel drive) and/or the component-specific areas were then produced with the help of incremental sheet metal forming. So as to be able to manufacture fault-free drive consoles (that is, drive consoles without wrinkles and cracks), extensive systematic investigations were required in order to be able to define appropriate machining strategies and process parameters. The need in so doing to take the whole of the process chain into consideration was evident from the fact that the design of the universal blank has a radical effect on the final forming result. The result of the studies was to demonstrate that, by means of this combination of processes, the process chain for manufacturing the two component variations could be significantly shortened and the number of forming tools required reduced from 5 tools each to 3 tools each per component. 4.2.4 Substitution of Thermal Jointing Operations In bodywork manufacture, the substitution of thermal jointing operations by forming-based jointing processes (e.g. clinching) also offers the potential to significantly reduce the amount of energy used during the production process. The omission of heat means a lower energy requirement and leads to improvements in the achievable form and dimensional accuracy of the components. Taking thick sheet clinching (e.g. as used in the construction of commercial vehicles) as an example, the potential for reducing energy consumption by comparison to a thermally assisted connection (e.g. MAG welding) was determined analytically in the basic investigations. Taken as the reference value here was the value of the joint energy obtained (energy input per unit of strength) which, in the medium to long term, may also be applied as a significant parameter for the energetic evaluation of industrial jointing processes. Calculations show that the amount of energy under static load required to achieve a corresponding level of strength using clinching instead of the thermal process is only around one third (Fig. 6). thermally

mechanically

energy per strength 150 J/kN

3

50 J/kN

:

1

:

1,7

flange dimensions

1 need for research

- identification of application areas - integration in process chains

Fig. 6 Saving energy by process substitution [2]


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The dynamic load on joints represents an additional aspect. Since motor vehicle structures are designed to cope with cyclic strength and because clinched as opposed to welded joints demonstrate a significantly better response to cyclic load, it may be assumed that the joint energy obtained from clinched joints as opposed to thermal processes can be reduced still further. In this phase of the investigations it should be pointed out that, for these initial considerations, possible further aspects such as e.g. accessibility have for the present been disregarded.

4.3 Resource Efficiency in Tool Making 4.3.1 Flexible Geometry Tool Principle “System Module” The development and implementation of modular tool systems for the flexible manufacture of bodywork parts represents a further approach to energy and resource efficiency in automotive production. At the same time, the objective is to manufacture a range of tooling components by utilising and re-assembling tooling components. Using this approach it will be possible to significantly reduce the consumption of materials and energy for manufacturing forming tools and this procedure is particularly suitable for the manufacture of internal structural parts. The above-mentioned joint project was carried out in collaboration with various industrial enterprises under the leadership of BMW AG [3, 8]. In the project, the process capability of a “system module“ (Fig. 7) for manufacturing a range of seat crossmembers using forming technology underwent a theoretical assessment. Its potential in terms of re-configurability and recyclability of existing tooling components for the manufacture of derivatives in the “seat crossmembers” family of components was evaluated. At the same time it was established that 80% of the components in the basic structure as well as up to 50% of the tool active parts can be re-used for the manufacture of crossmember derivatives. The prototype of a

part-specific, tool-related

unified part geometry Fig. 7 System module

not toolrelated

basis tool

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tooling system of this kind is currently undergoing extensive tests at the Fraunhofer IWU in Chemnitz with a view to providing evidence of the effects as regards recyclability and sustainability, including in practical application. 4.3.2 Use of Active Media The use of active media and energies (e.g. elastomers, fluids, gases, electromagnetic fields ...) in forming processes offers, by comparison to traditional forming, advantages in terms of • the achievement of high levels of deformation, • guaranteeing a high form and dimensional accuracy (reduction of springback behaviour), • guaranteeing high levels of component rigidity and • the integration of additional forming, cutting and jointing operations into the main forming process. In addition, and especially in conjunction with the manufacture of forming tools, an opportunity is provided to significantly increase resource efficiency because the active media used assume the functions of tool active parts, thus enabling savings to be made in relation to parts of this kind. In active media-based sheet metal forming, the medium assumes, for example, the function of a forming punch which means that the design of the forming tool can be considerably simplified and the amount of material that needs to be used as well as the processing expenditure can be significantly reduced.

basis: uniform part geometry

PART I

PART II

Fig. 8 Flexible part manufacturing using gas generators

One innovative example of the use of active media is the use of gas generators that are responsible for triggering airbags and, in conjunction with this, generate corresponding volumes of gas within very short time units. By way of follow-up to this basic idea, investigations are underway at the IWU in Chemnitz to establish whether this technology can be used both for cutting and for forming processes (Fig. 8).


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In gas pressure cutting, the gas takes over the function of the cutting punch. Based on an appropriate tool principle and the way in which the gas is conveyed to the cutting zone, perforating and trimming operations are possible outside the main effective direction of the press which have hitherto only been possible using expensive tooling and tapered slide valve technology. In addition to the positive effects in reducing the complexity of the tooling technology required, it is also possible by integrating gas pressure cutting into forming operations to achieve not only a considerable shortening in process chains but also to guarantee a high quality cut surface due to the effects of high speed [3, 9, 10].

4.4 Efficiency Facilities Even the use of low energy forming machines in bodywork parts production will lead to an increase in efficiency and hence resource efficiency. One approach consists in the extensive avoidance of “lost energy“ through the deployment of closed resource cycles (Fig. 9). One example of this is the development of energy-saving die cushions for forming presses. The present-day cushion systems are mainly based on the principle of displacement. Functioning as an actuator here is a hydraulic valve that acts as hydraulic resistance. The total output of the displacement device is converted into dissipated energy at the valve and this leads to heating of the fluid, thus making additional cooling necessary. As part of a project with BoschRexroth, a principle for an energy-saving die cushion has been developed which considerably reduces lost energy [2, 5]. Here a variable displacement pump is used as an actuator and this can also operate as the motor. The principle is based on the fact that the output of the displacement device minus the transformer losses is converted into mechanical energy at the pump shaft. This mechanical energy can either be stored (flywheel) or fed back as effective power into the electricity network via the motor (in generator operation). Solution Approach Leistungseintrag input

recovered Rückgewonnene Energie energy

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energy verlustloss main drive Hauptantrieb

Leistungsperformance loss verlust Energierückenergy recovering gewinnung

forming Umformwork arbeit Leistungsenergy verlust loss Kissen

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Energy Savings up to 65 % (in comparison with conventional cushions)

Fig. 9 Production of closed resource cycles –energy-saving die cushions

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The recouped power can then be absorbed simultaneously by the main drive of the forming machine and this will ultimately reduce the amount of power taken from the network. Current experimental studies have indicated that up to 65% of power input can be recouped for certain load ranges.

5 Summary The technological applications show that a large number of options exist for increasing resource efficiency in bodywork manufacture. Using efficiency technologies means that there is potential not just for reducing the amount of energy consumed by the motor vehicle in drive operation. In addition, an opportunity also emerges for reducing material deployment on the one hand and the amount of energy required for the production of components on the other. However, an essential pre-condition is the need to consider the process chain as a whole and to take account of all interactions between the individual components. • the implementation of new construction methods involving the use of innovative lightweight construction materials and semi-finished goods so as to guarantee optimum material utilization, • consistent shortening of process chains on the basis of resource-optimised technologies and process combinations, • guaranteeing maximum process reliability so as to reduce scrap and reworking or • the use of highly flexible and reconfigurable low energy production systems and facilities. References [1] Hoffmann, C.: Kumulierter Energieaufwand und optimierte Nutzungsdauer von Personenkraftwagen. IfE Schriftenreihe. Heft 31. TU München (1996) [2] Neugebauer, R. (ed.): Energieeffizienz in der Produktion. Untersuchung zum Handlungs- und Forschungsbedarf. Abschlussbericht (gefördert durch das BMBF). Fraunhofer-Gesellschaft (2008) [3] Neugebauer, R., Sterzing, A.: Ressourceneffiziente Umformtechnik. In: Proceedings of the 5th Chemnitz Car Body Colloquium, Chemnitz, Germany, November 11-12, pp. 81–95 (2008) [4] Neugebauer, R., Bräunlich, H., Scheffler, S.: Process Monitoring and Closed Loop Controlled Process. In: Proceedings of the International Conference and Exhibition on Design and Production of Machines and Die/Molds, Cesme, TurKey, June 21-23, pp. 279–287 (2007) [5] Neugebauer, R., Bräunlich, H., Kräusel, V.: Umformen und Schneiden mit Hochgeschwindigkeit – Impuls für die ressourceneffiziente Karosserieteilbearbeitung. In: Proceedings of the 5th Chemnitz Car Body Colloquium, Chemnitz, Germany, November 11-12, pp. 205–213 (2008)


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[6] Neugebauer, R., Bräunlich, H., Scheffler, S.: Process Monitoring and Closed Loop Controlled Process. In: Proceedings of the 1st International Lower Silesia-Saxony Conference AutoMetForm, Wroclaw, Poland, May 6-9, pp. 21–41 (2008) [7] Neugebauer, R., Sterzing, A., Müller, R., et al.: New Approaches for the Characterization of Sheet Materials – A Precondition for the Use of New Sheet Materials and Forming Processes. In: Proceedings of the 9th International Conference on Technology of Plasticity, Gyeongju, Korea, September 7-11, p. 106 (2008) [8] Neugebauer, R., Kräusel, V., Weigel, P., et al.: Adiabatic Cutting – Use of High Speed for Resource-Efficient Manufacturing. In: Proceedings of the 7th Internation Conference on Industrial Tools and Material Processing Technologies, Ljubljana, Slovenia, October 4-7, pp. 97–100 (2009) [9] Neugebauer, R., Sterzing, A., Bräunlich, H., et al.: Resource Efficiency in Tool and Die Making – Chances for Competitiveness. In: Proceedings of the7th Internation Conference on Industrial Tools and Material Processing Technologies, Ljubljana, Slovenia, October 4-7, pp. 3–8 (2009) [10] Neutz, J., Ebeling, H., Hill, W., et al.: Application of Pyrotechnic Gas Generators in Sheet Metal Forming Technologies. In: Proceedings of the 9th International Symposium and Exhibition on Sophisticated Car Occupant Safety Systems, Karlsruhe, Germany, December 1-3, pp. 17/1–17/15 (2008) [11] Roscher, H.J., Neugebauer, R., Wolf, K., et al.: Control of Sheet Metal Forming Processes with Piezoactuators in Smart Structures. In: Proceedings of the International Conference Smart Structures and Materials and NDE for Health Monitoring and Diagnostics, San Diego, USA, February 27-28 (2009) 2006.paper 61710E

Self-Tracking Order Release for Changing Bottleneck Resources Matthias Hüsig

Abstract. In this paper a self-tracking order release strategy for job shop production with well-defined routes is presented. The release strategy is a combination of different known methods. The changing machine loads, caused by the different products manufactured in the job shop, are compensated. Additionally the constraint of the due date of each individual order is kept. Balanced load on all machines is achieved by controlling the sequence of released order and the release times. For the adjustment of the controller only the average WIP (Work in Process) of each machine has to be set. The strategy is tested with two plant models implemented as Petri net simulations.

1 Introduction Consider a flexible job shop where a multiplicity of distinct orders is processed using machines on different routes. Each order is produced within a defined sequence of process steps. The sequence of the process steps is stored in the process plan. With this the orders are routed through the job shop on one defined way. If several orders are in a buffer in front of a machine, a sequencing rule decides which order is produced next. In this job shop every machine buffer releases the orders with the FIFO (First-in-First-Out) principle. A machine can process only one order mutually exclusive at a time. This situation is shown in Fig. 1 where two kinds of orders (A and B) are produced in one plant. The process plans guide both kinds of orders on different routes through this plant. Machine 1 accomplishes the first production step for both kinds of orders; the second is accomplished by machine 2 and 3, respectively. Orders with different routes lead to a dynamic variation of buffer loads of subsequent machine buffers in the job shop. In the given example the buffer loads of machine 2 and 3 changes with a delay after release of job A and B, respectively. Matthias Hüsig Institute of Automation, Hamburg University of Technology, 21073 Hamburg, Germany e-mail: [email protected]

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M. Hüsig released orders A, B

plant

buffer 1

machine 1

material flow

buffer 2

buffer 3

machine 2

machine 3

finished order A

finished order B

Fig. 1 Material flow diagram of the plant. After the release of orders A and B they are processed on machine 1 first. Then the orders of the type A are processed on machine 2 and orders of the type B are processed on machine 3.

This delay is made up of the processing time in machine 1 and a queue time in the buffer of the particular machine. For this example, it is difficult to control the loads of buffer 2 and 3 because of different delays at machine 1. In this paper a production control method is described which achieves two targets — it reduces dynamic load fluctuation in machine buffer and keeps to the due dates as far as possible, with low work in process (WIP) in the whole plant.

2 State of the Art The normal CONWIP (Constant Work in Process) [5] release rule leads to a constant WIP in the whole job shop. However different types of orders lead to different loads of the machines. This happens even if the occurrence of both kinds of orders is uniformly distributed over time. Workload control is used to get a high efficiency of the whole production. Realignment of orders depending on the algorithm controlling the workload can lead to violations of the due dates of the individual orders. The calculation of the optimal release sequence achieving both goals need a lot of calculation time and can be done via mixed integer linear programming (MILP) [2, 9]. This calculation method is not part of this paper. In this paper, only methods usable for online dispatching are inspected. Online dispatchers detect shifting bottlenecks and control the workload of all machines in the job shop. This should work also for cyclic behavior with multiple uses of certain machines during production. Workload control and order release strategies are an ongoing subject of scientific research [8, 11, 7]. The strategies balance different and conflicting objectives in production control. For each objective there exist different release strategies. The workload of the machines can be controlled e.g. by WIPLOAD [12], CONWIP [5],

Self-Tracking Order Release for Changing Bottleneck Resources

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CONLOAD [10] or other workload balancing control mechanisms like starvation avoidance [6]. With the sequence of order releases the lateness of orders and other production objectives can be controlled. Two of these are the balanced workload of the machines and the due date of the single order. All related production rules try to minimize the throughput time and try to achieve high machine utilization. In research not only workload control is a topic but also the detection of the current bottleneck resource [11, 3]. Single parts of the controller algorithm presented in this paper are known, but the different combination of rules leads to new effects like adaption of stock levels and machine load.

3 Scheduling Algorithm In production planning several conditions have to be considered by the rules of the controller. Two most important conditions are the workload and the due date. The order release has an influence on both values. The algorithm is divided into two parts. In the first part, the decision is made which order will be released next. In the second part, the release time is determined. The automatic selection and release is used for self tracking the load of the machines over time with respect to the due date.

3.1 WIP Stretch Definition Normal load balancing algorithms as described in [13] and [1] use the WIP of a single machine controlling the order release. If the WIP of the bottleneck machine exceeds a lower limit, orders using this machine will be released next. A production line behaves like a time delay system. It is difficult to calculate the delay of each order arriving at a certain machine exactly because orders have different production times and particularly different idle times in the buffers of the machines. This is the reason why the WIP of a production facility is stretched to all facilities before. This approach is similar to the workload control of Land and Gaalman [7]. After order release the workload of all machines is increased. With this procedure the future load of machines in the job shop can be estimated. The predicted load of the machine increases depending on the process step. It is devaluated by dividing the WIP by the number of process step. The predicted workload for orders guided on routes through the production are calculated before release, by summing up all machine WIP stretches of machines used on this route. Table 1 shows an example of the calculation for the increase of the WIP stretch of the machines used during production. The online calculation of the WIP stretch of each machine can be done in a similar way. Released orders increase only the WIP of the first machine, but the WIP stretch increases for every machine used during production. The WIP stretch of the machine increases by a Δ of the WIP of a particular job i at the process step k of route j divided by the process step:

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Table 1 Example for WIP stretch calculation used work stations

process step

real workload

Δ WIP stretch

2 1 3

1 2 3

100 80 90

100\1 = 100 80\2 = 40 90\3 = 30

W IPi,k (1) k If an order is released the WIP stretch increases for all following machines according to (1). This being the case the WIP stretch has to be reduced by the same value if an order finishes a process step at a machine. The new WIP stretch of a ma chine W IPstretch (i, j) (2) has to be updated by order release and by finishing a prok cess steps at a machine. It is calculated by adding and subtracting respectively the Δ W IPstretchk (i, j).

Δ W IPstretchk (i, j) =

(i, j) = W IPstretchk (i, j) ± Δ W IPstretchk (i, j) W IPstretch k

(2)

To calculate the expected average WIP stretch (W IPstretch j ) for a route j all WIP stretches of the machines are summed up and divided by the number of process steps N of route j. N( j) W IPstretchk (i, j) ∑ (3) W IPstretch j = k=1 N( j) The number of the process step is included to accommodate the different length of the routes.

3.2 Sequencing Rule Order release and in particular the sequencing use the average WIP stretch of each order from (3) to chose the next release candidate. The average WIP stretch of an order captures the predicted workload for all machines which will be used during production. The scheduling algorithm should release orders which pass through machines with low workload and procrastinating orders which pass through machines with high workload. If the orders in the plant are processed on different machines, or on the same machines on other routes, the load of the machines in the shop can be balanced. A high average WIP stretch of one particular type of order shows that machines which will be used suffer under high workload. In contrast to this low average WIP stretch shows that the machines have a low workload and with this the order will have a short throughput time. On this way the scheduling algorithm avoids starvation and overload of the machines as far as possible. Up to here, the algorithm considers only the workload of the machines. To consider the due date of a single order the algorithm is enlarged to keep the due date.


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The average WIP stretch is combined with a time factor (T F). To calculate the time factor the remaining time for production of the job must be calculated first. The urgency of a job is represented with the release buffer time (RBT ). This is the time per process step N( j) being left for production; this is the throughput time corresponding with the sum of the WIP stretches. With the current time τ and the due date DD the release buffer time for job i on route j can be calculated as follows: N( j)

RBTi =

DDi − τ − ∑k=1 W IPstretchk (i, j) N( j)

(4)

The RBT can assign positive and negative values depending on the delay of the order. For the release rule a time factor is needed which represents the possibility to suspend the release of an order to get a better load balance in the whole plant. The algorithm should prefer orders with a near due date and ignore the due date if there is enough time left for workload balancing. This is gained by taking the logarithm of the RBT . For delayed orders the RBT reaches negative values, but the domain of the natural logarithm is only the positive numerical range. Therefore two cases are separated: ln(RBTi + 1) for RBTi > 0 T Fi = (5) RBTi else. To get a continuous curve the argument of the logarithm is incremented by 1 for the case of positive RBT . The final scoring factor (SF) for the release decision is a multiplication of W IPstretch and T F. For all orders left in the stock SF is calculated. The order i with the smallest value SF is released next. SFi = min(W IPstretchi × T Fi ) i

(6)

This factor includes the predicted load and a time factor for the particular order. The order with the smallest SF leads to a good combination of load balance and due date adherence for the present plant workload situation.

3.3 Release Time Both the sequence, as well as the release time has an influence on the workload of the machines. When orders are released too early, this leads to a heavy workload, and then to less planning flexibility. For late releases, bottleneck resources may suffer from disruptions of material flow. Due to the different routes of orders produced in the job shop they do not have the same influence on the load of each machine, however for this reason starvation of a machine with little load cannot be avoided. The release time is calculated with only the load of the local bottleneck resource in mind. This tends to result in a high workload but not a good efficiency. For the following calculations the bottleneck resource m for order i must be detected. The

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bottleneck is the resource with the maximum WIP stretches of all k resources used by order i: W IPstretchm (i, j) = max(W IPstretchk (i, j)) k

(7)

For the bottleneck resource the execution time (ET ) is calculated. The WIP stretch of the local bottleneck will be the same over a long time if we use the execution time as release time. To control the WIP stretch to the given set point the release time can be shortened or enlarged. If the WIP stretch is lower than the given set point the release time must be shorter. To reach the set point of the WIP the release time is scaled by a quotient of WIP stretch at the bottleneck divided by set point WIP stretch (W IPsp ). The release time is computed by adding the scaled execution time by the present time τ : RT = τ + ET

W IPstretchm (i, j) W IPsp

(8)

The load of different bottleneck resources is controlled by selecting the next order depending on the T Fi and scaling of the release time (RT ) automatically. After the release time is expired the order is released and the WIP stretch will be updated. The algorithm is restarted and the smallest average WIP stretch of the remaining orders is calculated.

4 Scheduling Example In order to evaluate the scheduling algorithm it is tested with the plant described in Fig. 1. A production of 500 job orders is simulated using a Petri net based simulator similar to [4]. Each order has some attributes storing the lot size, due date and route number, respectively. The distribution of the attributes ’due date’ and ’lot size’ is uniform in between defined limits (Tab.2). The routes are uniformly distributed among both kinds of orders A and B, respectively.

Table 2 Attributes for the orders in the scheduling Example attribute

min

max

due date [in days]

1

5

lot size in one job

1000

3000

In Fig. 2a the overall production time is plotted with respect to the WIP of the whole plant. It shows two curves representing different dispatching rules; the dotted curve represents the CONWIP rule and the solid line the WIP stretch rule. Each curve arises from a series of simulations with an increasing WIP in the whole plant.


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The dotted curve shows a declining overall production time approaching a lower limit. For good machine utilization the WIP can be increased. High WIP leads to low overall processing times and a good adherence to due dates. Contrary to the CONWIP rule the WIP stretch rule leads to a shorter overall processing time for all load levels. The solid line of the WIP stretch rule approaches very fast the minimum value of the overall production time. This means optimal performance can be achieved even with little WIP, if the WIP stretch algorithm is used. If the orders are scheduled with the CONWIP rule the WIP of this method must be more than 8 times higher to get near equal overall processing time. In Fig. 2b the resulting numbers of delayed orders are plotted with respect to WIP. It can be seen that even for high WIP it is not possible to hold the due date for all orders using the CONWIP rule. Contrary to the CONWIP release rule the WIP stretch rule can hold the due date for all orders already with low WIP. In addition to Fig. 2, each individual machine load over time is plotted in Fig. 3 in order to understand the different behavior of the plant. The average WIP of the whole plant is equal to 12, for the simulation data in which both methods are compared. In the diagrams in Fig. 3, the WIP of the machines are shown resulting from the different release strategies. On the on hand with the index 1 the CONWIP controlled, and on the other hand with index 2 the WIP stretch controlled ones. Fig. 3a) shows the overall WIP with respect to time. It can be seen, that the WIP for the CONWIP rule is exactly 12. This is due to the fact that WIP is limited to a maximum load to make it comparable to the WIP stretch rule. The WIP stretch rule tunes itself with the correct parameter to this average WIP. It is obvious that the overall processing time is shorter for the WIP stretch rule than for the CONWIP rule. Fig. 3b)–d)

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show the WIP with respect to time for the buffer in front of each machine. Machine 1 is well utilized with both scheduling algorithms, because there is no break of the material flow. But this does not apply for machine 2 and 3, respectively. They run idle because of loss of required jobs Fig. 3c1)–d1). If machine 2 runs idle machine 3 has heavy load and vice versa. The curves of the WIP run in opposite direction, seldom both machines work at the same time. The CONWIP release strategy leads to a good load for machine 1. Machine 2 and 3 suffer under altering load utilization. If a break at the material flow appears the productivity decreases. The WIP of machine 2 and 3 has got a very dynamic character controlled with the CONWIP rule. The WIP increases and decreases on a short time scale. These fluctuations cannot be prevented with higher load. In contrast, the WIP stretch rule smoothes the WIP for machine 2 and 3, respectively. It leads to constant workload, short overall production time and a good adherence to due date Fig. 3c2)–d2).


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5 Industrial Scheduling Application For further verification the scheduling rule is also tested with an industrial application which is more realistic. The job shop consists of 4 work groups (WG) each with two machines. Jobs produced in this plant are routed through the shop on 7 different routes. The decision which machine in a work group is used for a job is defined by the attributes ’material’, ’color’ or ’size’ of the order. Orders have two additional attributes which store the due date and the production quantity. The order pool consists of 500 different types. New orders reach the order pool statistically. Orders are released with the described online release rules dependent on the orders in the present order pool. This industrial application shows similar behavior (Fig. 4) as the model from section 4. The overall production time decreases with a growing WIP in the plant similar to the scheduling example and approaches a lower limit (Fig. 4a). For a high WIP both methods approach to the same limit. In Fig. 5 the WIP of all machines

Table 3 The order of machines defined by the different routes R1

R2

R3

R4

R5

R6

R7

1 2 3

WG2 WG1

WG3 WG4 WG1

WG1 WG4

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WG1 WG3

overall production time

process steps

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a)

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40

50

Fig. 4 a) Overall processing time for all orders with respect to WIP of the whole plant. b) Percent of delayed orders with respect to WIP of the whole plant.

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Fig. 5 Comparison of the resulting WIP, depending on whether the production is controlled by the CONWIP (upper part of each subfigure) or WIP stretch method (lower part of each subfigure). Machine group 1 to 4 consists of 2 machines with average WIP of 12 orders in the entire plant.

is plotted with respect to time. In this simulation the average workload is 12 orders for both release rules. The overall production time is far shorter for the order release using the WIP stretch rule than order release using the CONWIP rule, resulting from a balanced WIP of all machines in the plant. The upper curve simulated with the CONWIP rule show altering WIP in short intervals for all machines. Break of material flow appears also with the WIP stretch rule, but not as often as it appears with the CONWIP rule.

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Additionally the algorithm is tested for robustness against sudden machine breakdown. As an example a breakdown of machine 1 for 480 time steps is simulated (Fig. 6). The WIP is increased just a little after breakdown for a short time. The breakdown has only less influence on the inventory of each machine as shown in Fig. 6. After breakdown the average WIP stretch for orders using machine 1 increases. Hence such orders will be restrained and will not be released.

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6 Conclusion The presented order release strategy can easily be implemented for complex job shop problems with altering routes. The algorithm leads to a short over all processing time, and a good adherence to due dates. A low WIP gives the planner of the plant more flexibility. It can also be used for cyclic job shop problems with multiple use of the same machine. As a consequence of the load balancing principle the algorithm has a smooth response of manufacturing disturbances and machine breakdown.

References 1. Bechte, W.: Controlling Manufacturing Lead Time and Workin-Progress Inventory by Means of Load Oriented Order Release. In: American Production and Inventory Control Society, Conferences Proceedings (1982) 2. Brucker, P.: Scheduling Algorithms, 4th edn. Springer, Berlin (2004) 3. Cheng, H.-C., Chiang, T.-C., Fu, L.-C.: Multiobjective job shop scheduling using memetic algorithm and shifting bottleneck procedure. In: IEEE Symposium on Computational Intelligence in Scheduling, CI-Sched (2009), doi:10.1109/SCIS.2009.4927009 4. von Drathen, A.: Compact modeling of manufacturing systems with petri nets. In: IEEE International Conference on Systems, Man and Cybernetics ISIC, pp. 3487–3492 (2007), doi:10.1109/ICSMC.2007.4413580 5. Enns, S.T., Rogers, P.: Clarifying CONWIP versus push system behavior using simulation. In: Simulation Conference, WSC 2008, pp. 1867–1872 (Winter 2008), doi:10.1109/WSC.2008.4736277 6. Glassey, C.R., Resende, M.G.C.: Closed-loop job release control for VLSI circuit manufacturing. IEEE Transactions on Semiconductor Manufacturing (1988), doi:10.1109/66.4371 7. Land, M., Gaalman, G.: Towards simple and robust workload norms. In: Proceedings of Workshop on Production Planning and Control, pp. 66–96 (1996) 8. Land, M., Gaalman, G.: Workload control concepts in job shops A critical assessment. International Journal of Production Economics 46(7), 535–548 (1996) 9. Leung, J.Y.-T.: Handbook of Scheduling, Algorithms, models, and performance analysis. Chapman & Hall/CRC, Boca Raton (2004) 10. Rose, O.: CONLOAD-a new lot release rule for semiconductor wafer fabs. In: Proceedings of the 31st conference on Winter simulation, pp. 850–855 (1999), doi:0.1109/WSC.1999.823297 11. Roser, C., Nakano, M., Tanaka, M.: Shifting bottleneck detection. In: Simulation Conference (2002), doi:10.1109/WSC.2002.1166360 12. Qi, C., Sivakumar, A.I.: Job release based on WIPLOAD control in semiconductor wafer fabrication. In: 8th Electronics Packaging Technology Conference, EPTC 2006, pp. 665–670 (2006), doi:10.1109/EPTC.2006.342793 13. Wiendahl, H.-P.: Load-Oriented Manufacturing Control. Springer, Berlin (1995)

Integrated Operational Techniques for Robotic Batch Manufacturing Systems Satoshi Hoshino, Hiroya Seki, Yuji Naka, and Jun Ota

Abstract. This paper focuses on a batch manufacturing system with multiple industrial robots. Inappropriate coordination of the robots might cause a bottleneck. In addition, a bottleneck is a constraint that dominates the entire system performance, that is, the productivity. Therefore, for an efficient system, these robots are required to operate appropriately while relating to each other. This is a challenge in this study. We propose the following operational techniques: route planning approaches and operation dispatching rules on the basis of task-assignment that will reduce the effect of a bottleneck. Furthermore, reactive cooperation, so that the robots respond to a fluctuating heavy workload caused by the shifting bottleneck, is an essential operational technique. Throughout the simulation experiments, each combination of the operational techniques is examined; finally, the integrated operational techniques are shown.

1 Introduction Generally, in manufacturing systems for high-mix low-volume production, a number of different machines are operating. In order to improve the throughput of the whole of the operation in the system, it is not enough to use each of the machines efficiently, but an efficient coordination technology, based on the careful consideration of the operations of all the machines, is required. A pipeless batch manufacturing plant in chemical process industries is an applicable environment of a flexible batch manufacturing system from the standpoint of the reasonable and multi-product production of chemical products, such as Satoshi Hoshino · Hiroya Seki · Yuji Naka Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama 226-8503 Japan e-mail: [email protected] Jun Ota Research into Artifacts, Center for Engineering (RACE), The University of Tokyo

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lubricants, adhesives, pharmaceuticals, paints, and inks, in addition to adaptation to a fast-changing market. The reason for this trend is that materials are transported by movable vessels and production processes are conducted at a number of fixed process stations. Thus, compared to a general batch manufacturing plant, which consists of a pipe network, a pipeless batch plant is able to prevent material contamination when materials or products are switched from batch to batch. Furthermore, each recipe for a production process is different from others; herewith, a multi-product production in one plant is made possible. However, since advanced coordination technology for the equipment is required, only a few plants have started operations so far. With regard to this issue, we focus on a robotic batch manufacturing system. Each industrial robot is able to perform a task agilely according to its control law and to respond to the changing circumstances flexibly by sharing information via communication. In this regard, let us notice that a manufacturing system is usually located in a closed plant facility; thus, a heavy workload for a robot that arises from a bottleneck at a place in the system affects productivity as a whole. Moreover, the bottleneck may shift to another place in the system even if it is corrected [1]. Therefore, for an efficient system, robots are required to operate appropriately while relating to each other and tracking the shifting bottleneck. We propose the following operational techniques: route planning approaches and operation dispatching rules on the basis of task-assignment that will reduce the effect of a bottleneck. Furthermore, reactive cooperation, so that the robots respond to a fluctuating heavy workload caused by the shifting bottleneck, is an essential operational technique. Throughout the simulation experiments, each combination of the operational techniques is examined; finally, the integrated operational techniques are shown.

2 Previous and Related Works Many previous studies that focused on pipeless batch manufacturing systems have addressed a production scheduling problem. The scheduling problem has been formulated mainly with the use of the Mixed Integer Linear Programming, MILP [2, 3, 4]. However, a main weakness of the MILP approach is that, as the complexity of a plant increases, the scheduling problem becomes very hard to formulate properly [5]. Huang et al., using constraint satisfaction techniques, have proposed an integrated scheduling methodology in consideration of the behavior of movable vessels [6, 7]. In industrial robotics, Yang et al. have proposed a robotic system that assists production in flexible manufacturing environments [8]. In the system, off-line robots work exclusively to support on-line robots. These previous and related works, however, have been based on the following assumptions: (I) fewer movable vessels with large capacity (≥10 [m3 ]); (II) fixed transport time of a vessel between process stations; (III) fixed operation (process) time at a station; (IV) a specific process equipment installed in every station; and (V) two categorized robots, directly operating and indirectly operating ones. Hence,

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(I’) it has been difficult to control the vessels agilely and flexibly; (II’) and (III’) as the case may be, an expected production volume according to the scheduling result is not achieved in the event that the vessel speed or the operation time at a process station fluctuates due to a disturbance [9]; (IV’) low system reconfigurability and multi-productivity result; and (V’) low resource utilization takes place due to these assumptions. In view of the above reasons, (I’) ∼ (V’) , in this paper, (I”) instead of a vessel, we use a large number of robots with small volume, namely, a material-handling robot with high mobility; (II”) and (III”) we take into account the actual robot’s behavior including uncertainty, i.e., variable moving and operation times; (IV”) instead of specific processing equipment, we use fewer movable robots, namely, materialprocessing robots, and the robots have various equipment; and (V”) both types of the robots perform tasks directly.

3 Challenges In this paper, there are two types of robots performing their own tasks, which are material handling and processing. These robots must cooperatively execute the assigned task. In other words, even if one robot’s efficiency improves, the other experiences a bottleneck and, as a result, a heavy workload. This phenomenon is a so-called shifting bottleneck, as described in Sect. 1. Of course, this workload sometimes occurs due to a bottleneck resulting from the given tasks and layout structure. Furthermore, since the heavy workload for the robot caused by the shifting bottleneck affects the overall system productivity, it is necessary to balance the fluctuating workload among the robots. To tackle the challenge, we propose the following operational techniques for the robots and synthesize the most efficient ones as integrated operational techniques. 1) Route planning for the material-handling robot; 2) operation dispatching for the material-processing robot; 3) task assignment to the robots; and 4) reactive cooperation among the material-processing robots depending on the situation.

4 Robotic Batch Manufacturing System In this decade, most new automated material-handling systems have usually been designed with a spine- or perimeter-type of configuration that formed a material flow loop within a plant facility [10]. Several layouts that have single-loop and cyclic structures have been reported [11, 12]. For this reason, we adopt a cyclic layout structure, as shown in Fig. 1. This layout is based on the well-known cyclic operations. In the system, the Material-Handling Robot (MHR) moves to transport materials and a product, and the Material-Processing Robot (MPR) moves among stations and conducts production processes, such as coupling, feed, blending, separation, discharge, and cleaning, at the stations.

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In order for the MHR to move agilely, three types of lanes, i.e., main (one-way), passing (one-way), and intermediate (two-way), are provided. Process stations are placed on the main lanes. Materials circulate through the process stations with the MHR; then, a final product is produced. Inside the main lanes, four bi-directional lanes for the MPRs are provided. Each MPR basically works at its own station (e.g., MPR 1 works at stations 1 ∼ 4). In this paper, assuming that each robot has a radio communication device, the robots are allowed to share and exchange information via distributed blackboards installed on them. This is a sign board model [13]. Using this communication model, the MHR is allowed to move on the lanes flexibly while selecting lanes and changing a suitable route to a destination, and the MPR is allowed to move to its own stations or other MPRs’ stations to support them depending on the circumstances. Each of the process stations, 1 ∼ 12, has a different property of a specific operation. At each station, it is impossible for an MPR to conduct a production process with two or more MHRs at the same time. Since the MPR provides varied equipment, such as a coupler, stirrer, reactive and separation meters, and a scrubber, the MPR is able to conduct all the production processes depending on a station. As for the discharging of a final product and cleaning of the MHR, these are the requisite processes in one batch; therefore, exclusive stations are set up for each of them. In


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5 Operational Techniques for the Robots 5.1 Route Planning for the MHR In order for the MHR to move adequately on the three types of lanes, we apply the following three route-planning approaches to the MHR: (a) shortest-path routing; (b) dynamic routing looking ahead to one station; and (c) dynamic routing looking ahead to all the stations to a destination. As for approaches (b) and (c), the breadth-first search method with an objective function regarding the distance to the destination is applied. Hence, the MHR does not detour any more than is necessary. In addition, these two approaches are repeatedly applied each time the MHR passes through a station and intersection on the planned route. Fig. 2 shows that MHR 1 is planning a route to the destination (goal station) from the current position (start station). At the start station, if MHR 1 plans a route to the goal station with the use of the shortest-path routing (a), it has to stop on the planned route due to impeditive robots, such as MHR 2 and MHR 3 (see Fig. 2(a)). On the other hand, by applying planning approach (b) to the MHR, MHR 1 determines whether an MHR is present at the next station via communication and then changes the lane to detour MHR 2 (see Fig. 2(b)). However, as shown in Fig. 2(c), MHR 1 needs to plan a route once again through the passing lane due to an obstacle, MHR 3. To avoid this waste of time, MHR 1 selects a route to the destination, as shown in Fig. 2(d), by planning a route with the use of planning approach (c) on the basis of the situation of all stations with regard to the destination.

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5.2 Operation Dispatching for the MPR MPRs 1 ∼ 3 work for the production processes at four stations, i.e., 1 ∼ 4, 5 ∼ 8, and 9 ∼ 12, respectively. Therefore, when multiple MHRs arrive at different stations (e.g., the 1st, 2nd, 3rd, and 4th stations) at the same time, it is required to appropriately dispatch the MPR (e.g., MPR 1) to the operations in order to improve the robot’s operating efficiency. For this purpose, we focus on the operation execution sequence among the MHRs and MPR; the MPR determines the next operation partner (MHR) and station on the basis of the following three dispatching rules: (a’) First-In First-Out (FIFO); (b’) nearest-neighbor; and (c’) minimization of the total moving distance using the full-search method. This execution sequence is repeatedly determined each time a task is finished according to the state of other stations if there is an MHR stopping at a station for the task. Fig. 3 shows a case in which, while an MPR is conducting the production processes to MHR 2 at a station, MHRs arrived at all other stations in the following sequence: MHR 4, MHR 1, and MHR 3. In this case, the MPR reciprocates to the right and left unnecessarily if rule (a’) is applied. On the other hand, the operations are performed smoothly in the following order: MHR 2 → MHR 3 → MHR 4 → MHR 1 by using rule (b’) and MHR 2 → MHR 1 → MHR 3 → MHR 4 by using rule (c’). These dispatching rules are, similarly, applied to MPR 4.

5.3 Task Assignment to the MHRs After an MHR is washed at the cleaning station, the next production recipe is assigned as a task to the MHR. In a material-handling system, task assignment policies for Automated Guided Vehicles (AGVs) have been proposed [14]; additionally, these assignment policies have been applied to a previous pipeless batch plant [15]. However, in the proposed heuristic rules, only the next destination of the AGV has been considered. In other words, a “single task [16]” has been assumed so far. In contrast, it is impossible to address an MHR equipped with a vessel and its content (materials or product) separately in the robotic batch manufacturing system. Moreover, each product is produced on the basis of its own recipe, which consists of a series of processes. All of the processes for one product are carried out by the same (one) MHR. Namely, this is a “multi task [16]” problem. Therefore, a suitable production task, in consideration of all destinations, needs to be selected from other tasks and then assigned to an MHR. For this purpose, we propose the following Material tank MHR 1

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objective function; a task (Taskk ) is assigned to the MHR based on the function. The objective function denotes that a task with the lowest similarity to the execution state of all the tasks in the system is assigned to the MHR. By doing this, a heavy workload due to the bottleneck that arises from the given tasks is made as uniform as possible. minimize ∑ ∑ Taskn,k (ExeTaskn − Taskn,k ), k

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where k is a reference task number and n represents a station number. ExeTaskn represents the total number of MHRs that are being and going to be processed at stations n following the production recipes. As for Taskn,k , a binary variable, 0 or 1, is given whether station n of the k-th reference task is a destination in the recipe for a product. In this regard, however, if a task is selected and assigned to an MHR by referring to all other unexecuted tasks on the basis of the objective function, tasks with fewer processes are gathered in the first half of the production activity, while tasks that have many processes remain in the second half. For this problem, we propose the following three assignment policies: (a”) in sequence (k = 1, 2, 3, · · · ); (b”) the whole task reference (∀k ∈ K); and (c”) a partial task reference (∀k ∈ K p ). By applying (c”), a batch is assigned to an MHR by referring to a limited number of unexecuted batches within a given range K p . Policies (b”) and (c”) are applied on the basis of the proposed objective function.

6 Simulation Experiment 6.1 Experimental Condition From Sect. 5.1, Sect. 5.2, and Sect. 5.3, in total, 3 × 3 × 3 = 27 combinations of the operational techniques are simulated. As a case study, the total number of tasks, K, is 200, and the process time at stations 1 ∼ 12 is determined to be 30 ∼ 80 [s] with a uniform distribution in a random manner. In the production recipe, a 0-1 binary variable is given by one-third and two-thirds for each station. If a 1 is given to a station, the MHR goes to the station. At the discharging and cleaning stations, 10 ∼ 40 [s] and 20 ∼ 80 [s] with a uniform distribution are required in a random manner. With regard to the assignment policy (c”) described in Sect. 5.3, the partial task reference range is 10 tasks (i.e., K p = 10).

6.2 Impact Evaluation of Each Operational Technique The system operation time with the use of the route planning, operation dispatching, and task assignment is shown in Fig. 4. This operation time is equal to the system throughput by dividing the time by the number of tasks, 200. In order to compare and evaluate the impact of each of the three techniques, (a) ∼ (c), (a’) ∼ (c’), and (a”) ∼ (c”), on the operating efficiency, for instance, the averaged operation time

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obtained through the simulations with fixed route planning (a), (b), or (c) and nine other combinatorial techniques ((a’) ∼ (c’) × (a”) ∼ (c”)) are shown in Fig. 4(a). We can see that the route planning approaches, (b) and (c), and task assignment policy, (c”), resulted in an efficient system regardless of the number of MHRs (see Fig. 4(a) and Fig. 4(c)). This result indicates that the synthesized operational techniques reduced the effect of the bottleneck and increased the production volume. Here, it must be noted that operational techniques with task assignment policy (b”) resulted in the most inefficient system (see Fig. 4(c)) due to the heavy workload caused by the given tasks. Moreover, while the operation time decreased as the number of MHRs increased from 5 to 10, the results of the operation time with 10 and 15 MHRs were almost the same. This is because that the fleet size was the factor that decides the throughput before the bottleneck occurred. To discuss the detail of this result, we analyze the robots utilization ratio.

6.3 Bottleneck Analysis In Fig. 5, as the robots utilization ratio, the sojourn time ratio of the MHRs (5, 10, and 15) at each station and the operation time ratio of the MPRs (1 ∼ 4) are shown on the basis of the combination of the operational techniques that achieved the given 200 tasks in the shortest time, namely, the best system. From the results of Fig. 5(a), Fig. 5(b), and Fig. 5(c), it is noticeable that the sojourn time ratio at the discharging and cleaning stations increases as the number of MHRs increases from 5 to 10 and then to 15. For this reason, the system throughput at the stations, 1 ∼ 12, increased as a result of the use of efficient operational techniques, and the MHRs often arrived at the discharging and cleaning stations in which no passing lane is provided. On the other hand, from a comparison of the results shown in Fig. 5(d), Fig. 5(e), and Fig. 5(f), it is evident that each MPR operated almost evenly. That is to say, in spite of the fact that all MPRs fully operated at their two or four stations, a bottleneck occurred at two stations due to the layout structure; eventually, MPR 4 had a heavy workload.


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In order to improve the bottleneck, it is general practice to add an MPR to the discharge or cleaning station. However, as discussed in Sect. 1, this is an insufficient approach to the shifting bottleneck. As a result, this approach probably induces a new bottleneck in another place. Therefore, it is obvious that reactive cooperation among the MPRs over their own process stations is necessary for the shifting bottleneck. In other words, if there is an MPR that has a heavy workload, other MPRs will support it by performing its task in order to balance the workload as called for by the particular situation.

7 Additional Operation Technique: Reactive Cooperation 7.1 Workload Balancing Tewolde et al. have proposed a distributed workload-balancing algorithm to assign tasks to robots evenly [17]. They, however, have assumed a single task under a static environment, and the proposed algorithm was thus executed only at the beginning of the operation. This is insufficient for a multi-task and shifting bottleneck. For such an environment, we have shown the effectiveness of reactive robot behavior [18]. Therefore, we focus on this robot’s reactivity for workload balancing, and we then propose the following reactive cooperation technique among adjacent MPRs. The detailed algorithm of the proposed technique is listed in Algorithm 1.

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Algorithm 1. ReactiveCooperation (MHR, MPR) 1: if f lagOperationMPRi = false then 2: if xMPRi = xSMPRi then 3: if xMHR = xSMPRi−1 then 4: if f lagOperationMPRi−2 = true then 5: Set NTMPRi ← Cooperation 6: else 7: if xT − xMPRi < xT − xMPRi−2 then 8: Set NTMPRi ← Cooperation 9: end if 10: end if 11: else if xMHR = xSMPRi+1 then 12: if f lagOperationMPRi+2 = true then 13: Set NTMPRi ← Cooperation 14: else 15: if xT − xMPRi < xT − xMPRi+2 then 16: Set NTMPRi ← Cooperation 17: end if 18: end if 19: end if 20: else 21: if xMHR = xSMPRi then 22: Set NTMPRi ← Maintain cooperation 23: else 24: Set NTMPRi ← Return to xSMPRi 25: end if 26: end if 27: else 28: if xMHR = xSMPRi then 29: Set NTMPRi ← Maintain cooperation 30: else 31: Set NTMPRi ← Return to xSMPRi 32: end if 33: end if

The MPR decides the cooperation to support other MPRs on the basis of the information of the MHR and other MPRs, MHR and MPR. MPRi represents the host MPR that has its own process stations, denoted as SMPRi . x shows a position; thus, xMHR , xMPRi , and xSMPRi represent the positions of the MHR, MPR, and its stations, respectively. xT is the position of the target station. Note that MPRi−1 and MPRi+1 are the MPRs adjacent to MPRi and SMPRi+1 and SMPRi−1 are their own process stations. f lagOperationMPR shows whether an MPR is operating (true represents operating, and f alse represents free). NTMPR indicates the next task of an MPR. If the MPR, MPRi , is free at its own station and an MHR arrived at the adjacent MPR’s station, xSMPRi−1 , the MPR begins to move to the station to support MPRi−1 if the other adjacent MPR, MPRi−2 , to MPRi−1 is operating. In this regard, we


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presuppose that the adjacent MPR, MPRi−1 , is also operating. If MPRi−2 is also free, a closer MPR to the target position begins the cooperation. In the same way, reactive cooperation among the MPRs, MPRi , MPRi+1 , and MPRi+2 , takes place if an MHR arrived at the adjacent MPR’s station, xSMPRi+1 . If MPRi is already at the adjacent MPR’s station, it stays at the station to support MPRi−1 or MPRi+1 as long as an MHR does not arrive at xSMPRi . If the MHR arrived at xSMPRi , MPRi returns to its own station. On the other hand, in a case in which MPRi is already operating at another MPR’s station, MPRi continues operating at xSMPRi−1 or xSMPRi+1 to support MPRi−1 or MPRi+1 if no MHR arrives at xSMPRi . If an MHR arrived at xSMPRi , MPRi returns to its own station after the current cooperative task. The MPR does not perform the reactive cooperation if it is operating at its own station.

7.2 Simulation Result Including Reactive Cooperation Table 1 shows the simulation result for 5, 10, and 15 MHRs. Under the “non-reactive cooperation,” the results in Sect. 6 are listed, and the other ones under “reactive cooperation” show the results including the reactive cooperation technique. In the columns labeled “best” and “worst,” the shortest and longest operation times are respectively described. Under the best and worst operation times, the combinations of the applied operational techniques are shown. From this result, we can see that the best and worst times with 5 MHRs obtained by using the reactive cooperation technique were 0.15 and 0.14 [h] longer than the results without the technique. The reason for this result is that no bottleneck occurred in this system; accordingly, reactive cooperation for workload balancing was not necessary. Therefore, the integrated operational techniques, when a small number of MHRs is used, are (b), (c’), and (c”) without reactive cooperation. On the other hand, the best and worst times are improved (10 MHRs: 0.27 and 0.68 [h], 15 MHRs: 0.66 and 0.87 [h]) as the number of MHRs increases by using the reactive cooperation technique. Furthermore, the best operation time with 15 MHRs is reduced by 0.43 [h] from the result with 10 MHRs. These results indicate that workload balancing for a shifting bottleneck was appropriately performed. The

Table 1 Simulation Result on the Operation Time

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Total operation time [h] Non-reactive cooperation Reactive cooperation Best Worst Best Worst 9.23 11.18 9.38 11.32 (b)(c’)(c”) (a)(b’/c’)(b”) (b)(b’/c’)(a”) (a)(b’/c’)(b”) 7.16 8.62 6.89 7.94 (b)(c’)(c”) (a)(a’)(b”) (c)(c’)(c”) (a)(a’)(b”) 7.12 8.27 6.46 7.4 (c)(b’)(c”) (a)(c’)(b”) (c)(c’)(c”) (a)(b’)(a”)

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Fig. 6 Robots Utilization Ratio with the Use of the Operational Techniques Including the Reactive Cooperation in the Best System ((·) indicates the number of MHRs)

integrated operational techniques for more MHRs are, therefore, (c), (c’), and (c”) with reactive cooperation. For the analysis of the bottleneck, Fig. 6 shows the robots utilization ratio with the reactive cooperation technique on the basis of the best result in Table 1. In a comparison of the results of Fig. 6(a) and Fig. 6(d) with the results of Fig. 5(a) and Fig. 5(d), the robots utilization ratio at each station is almost the same and even (about 25 [%]). For more MHRs, 10 and 15, workload balancing was performed sufficiently well with the use of the reactive cooperation technique; eventually, the shifting bottleneck around the cleaning and discharging stations (see Fig. 5(b) and Fig. 5(c)) was successfully improved, as can be seen in Fig. 6(b) and Fig. 6(c). Moreover, from the results of Fig. 6(e) and Fig. 6(f), the operation ratio of MPR 4 was reduced from 28 (see Fig. 5(e) and Fig. 5(f)) to 24 and 23 [%]. This is because the adjacent MPRs, 1 and 3, supported MPR 4; then, MPR 2 supported MPR 1 and MPR 3; eventually, heavy workloads among the MPRs were made uniform.

8 Conclusions In this paper, we focused on a robotic batch manufacturing system with a cyclic layout. In order for the robots, MHR and MPR, to operate appropriately while relating to each other, we proposed operational techniques, such as route planning for the


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MHR and operation dispatching for the MPR on the basis of task-assignment to the robots to reduce the effect of the bottleneck and increase the production volume, in addition to reactive cooperation technique among the MPRs for workload balancing. From the simulation results, we showed that these techniques could effectively improve the shifting bottleneck and evenly spread a heavy workload. Finally, integrated operational techniques depending on the number of MHRs were shown.

References 1. Roser, C., Nakano, M., Tanaka, M.: Comparison of bottleneck detection methods for AGV systems. In: Proc. of Winter Simulation Conf., pp. 1192–1198 (2003) 2. Bok, J.W., Park, S.: Continuous-time modeling for short-term scheduling of multipurpose pipeless plants. Industrial & Engineering Chemistry Research 37(9), 3652–3659 (1998) 3. Lee, K.H., Chung, S., Lee, H.K., Lee, I.B.: Continuous time formulation of shortterm scheduling for pipeless batch plants. J. of Chemical Engineering of Japan 34(10), 1267–1278 (2001) 4. Realff, M.J., Shah, N., Pantelides, C.C.: Simultaneous design, layout and scheduling of pipeless batch plants. Computers and Chemical Engineering 20(6), 869–883 (1996) 5. Huang, W., Chen, B.: Scheduling of batch plants: Constraint-based approach and performance investigation. Int. J. of Production Economics 105(2), 425–444 (2007) 6. Huang, W., Chung, P.W.H.: Scheduling of pipeless batch plants using constraint satisfaction techniques. Computers and Chemical Engineering 24(2), 377–383 (2000) 7. Huang, W., Chung, P.W.H.: Integrating routing and scheduling for pipeless plants in different layouts. Computers and Chemical Engineering 29(5), 1069–1081 (2005) 8. Yang, H.Z., Yamafuji, K., Arita, K., Ohara, N.: Development of a robotic system which assists unmanned production based on cooperation between off-line robots and on-line robots: Concept, analysis and related technology. Int. J. of Advanced Manufacturing Technology 15(6), 432–437 (1999) 9. Gonzalez, R., Realff, M.J.: Operation of pipeless batch plants - I. MILP schedules. Computers and Chemical Engineering 22(7), 841–855 (1998) 10. Peters, B.A., Yang, T.: Integrated facility layout and material handling system design in semiconductor fabrication facilities. IEEE Trans on Semiconductor Manufacturing 10(3), 360–369 (1997) 11. Sinriech, D., Tanchoco, J.M.A.: The segmented bidirectional single-loop topology for material flow systems. IIE Transactions 28(1), 40–54 (1996) 12. Guzman, M.C.D., Prabhu, N., Tanchoco, J.M.A.: Complexity of the AGV shortest path and single-loop guide path layout problems. Int. J of Production Research 35(8), 2083–2092 (1997) 13. Wang, J.: On sign-board based inter-robot communication in distributed robotic systems. In: Proc. of IEEE Int. Conf. on Robotics and Automation, pp. 1045–1050 (1994) 14. Egbelu, P.J., Tanchoco, J.M.A.: Characterization of automatic guided vehicle dispatching rules. Int. J. of Production Research 22(3), 359–374 (1984) 15. Gonzalez, R., Realff, M.J.: Operation of pipeless batch plants – II. Vessel dispatch rules. Computers and Chemical Engineering 22(7), 857–866 (1998)

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16. Gerkey, B.P., Mataric, M.J.: A formal analysis and taxonomy of task allocation in multirobot systems. Int. J. of Robotics Research 23(9), 939–954 (2004) 17. Tewolde, G.S., Wu, C., Wang, Y., Sheng, W.: Distributed multi-robot work load partition in manufacturing automation. In: Proc. of IEEE Int. Conf. on Automation Science and Engineering, pp. 504–509 (2008) 18. Hoshino, S., Seki, H., Naka, Y.: Development of a flexible and agile multi-robot manufacturing system. In: 17th IFAC World Congress, pp. 15786–15791 (2008)

A Mathematical Model for Cyclic Scheduling with Assembly Tasks and Work-In-Process Minimization Mohamed Amin Ben Amar, Hervé Camus, and Ouajdi Korbaa*

Abstract. In this paper, we deal with the cyclic scheduling problem. More precisely, we consider the cyclic job shop with assembly tasks. Such a problem is made of several jobs, each job consisting of tasks (assembly/disassembly tasks and transformation tasks) being assigned to machines in a cyclic way. This kind of scheduling problem is well fitted to medium and large production demands, since the cyclic behavior can avoid the scheduling of the whole tasks by considering only a small temporal window (cycle). Thus, cyclic scheduling is a heuristic to solve the scheduling problems whose complexity is NP-hard in the general case. Many methods have been proposed to solve the cyclic scheduling problem. Among them, we focus on the mathematical programming approach. We will propose here a mathematical model for cyclic scheduling with assembly tasks and Work-In-Process minimization, and we illustrate this approach with an example from literature.

1 Introduction Cyclic scheduling problems take place in different application areas such as compiler design, automated manufacturing systems, digital signal processing, railway scheduling, timetabling, etc. We will focus here on the automated manufacturing systems. In this domain, the production consists of cyclic jobs assigned to Mohamed Amin Ben Amar LI3 laboratory, ISG, University of Tunis, Tunisia e-mail: [email protected]

*

Hervé Camus LAGIS laboratory, EC Lille, Villeneuve d'Ascq, France e-mail: [email protected] Ouajdi Korbaa LI3 laboratory (ISG, Tunis), ISITCom Hammam Sousse, Tunisia e-mail: [email protected]

280

M.A.B. Amar, H. Camus, and O. Korbaa

machines. Each job consists of assembly/disassembly tasks and transformations tasks. The assembly tasks show the synchronization between operations, and the disassembly promote parallelism. This problem has to be optimized with regard to several criteria like throughput and Work-in-Process (WIP - the number of parts in the system). The WIP, which is an economic criterion, represents the intermediate stock. In the cyclic context, the throughput criteria will be replaced by minimizing the Cycle Time (CT). These two criteria are antagonistic. On one hand, to maximize the throughput, we have to use enough parts (WIP) to feed the bottleneck machine. On the other hand, with a few number of WIP (one for example) the resources will be pending for parts (in particle, the bottleneck machine(s)) and the throughput will not be optimized. Hence to take into account these two criteria, we will follow the resolution developed by Camus [4]. It consists of two phased approach. The planning step, which determine the optimal cycle time, and the scheduling step, which consists on minimizing the WIP while respecting the optimal cycle time (as a hard constraint). This approach ensures the existence of a scheduling, since a sufficient number of WIP allows to saturate the bottleneck1 machine(s). We focus here on the scheduling of operations in a precalculated cycle time, and we do not look for the best production ratios to be produced during a cycle time (an issue largely studied by Chrétienne [5] and Hanen [11]). In fact, we suppose that we know exactly what to produce during a cycle, which allows us to determine the optimal cycle time based on the workload of the critical resource. We are interested here in the cyclic scheduling problem with assembly tasks and Work-In-Process minimization. The remainder of this paper is organized as follows. In section 2, we will introduce systems with assembly/disassembly tasks, and we will propose a cyclic approach to solve these problems. In addition, we will define the WIP in these systems. In section 3, we will describe the mathematical model. In section 4, we will use an illustrative example in the literature to explain our approach. To conclude, we propose several perspectives to extend our work.

2 Cyclic Scheduling Problem with Assembly/Disassembly Tasks 2.1 Systems with Assembly/Disassembly Tasks The production lines of manufacturing system often include assembly/disassembly tasks. This can be accounted for the nature of the aimed output, which requires to

1

Machine with the maximum workload, i.e. machine m ∈ M for which the quantity

∑

( m , dij )∈OG

(d ij ) is the greatest.

A Mathematical Model for Cyclic Scheduling with Assembly Tasks

Disassembly task

281

Stage_1

Branches

Stage_2

Assembly task Stage_3

Fig. 1 Assembly/Disassembly problem

assemble and/or disassemble several parts ([13, 17, 18, 19, 20, 21]). There are also many systems with only disassembly tasks, for example disassembly lines used in recycling ([8, 10, 15]). We can also find a system with only assembly tasks (like [16]). In this context, the system must include the suitable resources able to perform these tasks. In these systems (“Fig.1,” [20]) there are three categories of operations: • Transformation tasks: affects the state of the pieces without adding extra parts in the system. • Assembly tasks: consists of assembling at least two parts to produce a new one. In this case, the number of parts in the system will decrease. • Disassembly tasks: consists of disassembling one piece to produce, at least, two parts. In this case, the number of parts in the system will increase. It follows that the precedence constraints of operations can be multiple. Which means that, with assembly, one task can have two or more predecessors. However, with disassembly one task can have two or more successors. Hence, we have to deal with non-linear job, which means that a job can include many branches.

282


We will consider here systems that contain only one disassembly operation and one assembly operation. The disassembly operation comes before the assembly one. Between these two tasks we will find at least two branches (on Stage_2 – “Fig.1”). Thus, the disassembly and the assembly tasks will delimit the different stages of the system (“Fig.1”). This choice can be viewed as a primary model type that takes into account the most important constraint which is encountered in assembly/disassembly systems: the synchronization of tasks. This choice can be justified by the need of simplification to start studying this scheduling problem. However, in future works, we will consider other types of models within extended constraints (like systems with several assembly and disassembly tasks and/or with imbricated stages).

2.2 Cyclic Behavior We propose to schedule a production plan, i.e. to determine the sequences of operations on resources and the time of lunching of each task. The schedule must be within the Cycle Time, and every cycle we produce one piece. The Scheduling problems are well known to be highly combinatorial. It has been shown that project planning problems are of polynomial complexity and that cyclic scheduling problems are NP-complete. Taking into account transformation tasks and assembly/disassembly one, makes the first problem NP-hard in most cases and keeps the second one in the NP-complete class. Hence, the use of heuristics is generally recommended. The scheduling of cyclic production system can be a possible solution to global scheduling. The answer to the total demand will be given by the repetition of a sequence known as cyclic scheduling. However, the optimal scheduling of a cycle does not guarantee the optimality of the total production, since the “the sum of optimal sub-paths is not necessarily an optimal path” [1]. That's why the cyclic behavior is still a heuristic. We can evaluate the performance of the cyclic scheduling by comparing the total time production with a lower bound computed from workflow analysis and the workload of the bottleneck machine. In this work, we suppose that the production and the optimal cycle time have been fixed in the planning step from workflow analysis and performance evaluation using Petri nets (Camus [4], Korbaa [14]).

2.3 Work-In-Process The aim of minimizing the WIP of a system is mainly due to the minimization of costs (intermediate stock, pallets design, and manufacturing). In factories, WIP levels between machines have capacity limits. This is mainly due to the limited physical space available to store the parts temporarily and the limits of the transport system. Also, if the number of WIP increases, it can produce a deadlock by overloading the system.


283

To understand the WIP in systems with assembly/disassembly tasks, we suggest to present this concept in linear jobs systems with (system within which each task has only one predecessor and one successor operation i.e. without assembly/disassembly tasks). In linear Job systems, the WIP represents the number of products in a system. Since there are no assembly/disassembly tasks, then every part in the system is bound to a single product. Moreover, many studies [3, 6, 7, 12, 14] ...) consider that parts remain clamped to their transport resource (for example pallet) during their entire journey in the system. Hence, minimizing WIP or the number of pallets is the same. However, the number of parts in systems with non-linear production line does not match the number of products. In fact, if we consider that we have to produce a “chair,” we have to assemble 6 parts: 4 legs, the back and the seating. This means that, after assembly, the number of parts changes from 6 to 1. Hence, the previous definition of WIP has to be reviewed. In this context, Fournier [9], has proposed a definition for the WIP. He supposes that all parts generated after a disassembly task or disappeared after assembly (i.e. parts which belong to the same product), represent only one WIP. Hence, if we consider a cyclic production system, and we suppose that there are several parts in the cyclic window which belong to x products, then, there is x WIP in the system. However, this definition does not consider the number of pallets in the system. In fact, we can find two schedules that present two WIPs, for example, the first schedule needs 10 pallets while the second requires 15 pallets. With this definition, we can not choose the first schedule (which needs less pallets) compared to the second one. Another point of view concerning the definition of the WIP is proposed by Trouillet [19]. He considers that the WIP in a system is equal to the maximum number of parts present in a cyclic window. In this paper, we will consider the definition of Trouillet, which aims to minimizing the maximum number of parts in the system. Moreover, we will consider that parts remain clamped to their transport resource (for example pallet) during their entire journey in the system.

3 A Mathematical Model for Cyclic Scheduling Problem with Assembly Tasks 3.1 Job Shop We use the following notations to define a job shop F. Machines: The set M = {m1, m2,…, m|M|} defines the set of machines of F. These resources are renewable and not shared by any operations. This means that they are reusable once they have finished the execution of a task and can only process one task at a time.

284


Operation: We define an operation of F using the machine m ∈ M as a pair (m,d) ∈ M × N* where d is called the duration of the corresponding operation. We denote by O∞ ≡ M × N* the set of possible (machine, duration) pairs. Job: We define a job g of the job shop F as a sequence of operations. Among these operations, we can find Assembly/Disassembly tasks. We denote by:

OG: set of all operations of the problem. Ei: Number of stages of the Job i. bi,j: Number of branches in stage j of the job i.

Eki , j : Number of operations in the branch k of the stage j of the job i. We denote operations by oki ,,lj , while i, j, k and l stands respectively for: the job, the stage, the branch and the index of the operation for the corresponding branch. s(i,j,k,l) = (I,J,K,L) where oKI ,,JL represent(s) the successor(s) of oki ,,lj . Job Shop: We define a job shop as a set of jobs G = {g1, g2, …, g|G|}. We denote by G the cardinal number of G, and we order the jobs of the job Shop by the formal parameter i∈a1, G b.

3.2 Cyclic Scheduling Problem The goal of cyclic scheduling is to schedule the cyclic pattern, within which each operation of the job shop is scheduled in a time range called cycle time. The optimal cycle time is defined as the sum of durations of tasks associated with the bottleneck machine(s). Since this optimal cycle time is reachable (we have to use enough parts: a WIP for each tasks in the system), classical scheduling problems consist in minimizing the number of pieces in the system for a given cycle time, equal to * Cmax = max ( ∑ (dij )). m∈M ( m, d )∈OG ij

* We will work here with a Cycle Time (CT) which is equal to Cmax . * CT = Cmax

3.3 Mixed Integer Programming Model We define below, “Fig.2,” a mixed integer programming model corresponding to the cyclic scheduling problem defined in Sect.3.2.

A Mathematical Model for Cyclic Scheduling with Assembly Tasks Minimize

∑

oki ,,lj ∈O G

285

( nb − 1) + (α si ,( ij,, kj ,,kl ,l ) + β si ,(ij,, kj ,,kl ,l ) ) s.t.: (1)

•∀ i ∈ a1,G b, ∀j ∈ a1,Ei b, ∀ k ∈ ced1,bi , j fhg , ∀ l ∈ cde1,E ki , j fgh ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ i, j ⎨t k ,l ⎪ ⎪t ki ,,lj ⎪ ⎪t i , j ⎪ k ,l ⎪t i , j ⎩ k ,l

* t ki ,, lj ∈ cde 0, C max − 1fgh

(2)

∈

{0,1}

(3)

β si ,(ij,, kj ,,kl , l ) ∈

{0,1}

α si ,(ij,, kj ,,kl , l )

sI , sJ − t sK , sL

−

i , j , k ,l B.α sI , sJ , sK , sL

(4)

≥ 1− B −

d ki ,,lj

(5)

i , j , k ,l i, j sI , sJ − t sK , sL − B .α sI , sJ , sK , sL ≤ − d k ,l sI , sJ − t sK , sL

−

(6)

≥

* C max

+1− B −

i , j , k ,l − B.β sI , sJ , sK , sL ≤ i, j I , J •∀ m ∈ M , ∀ok ,l , o K , L ∈ O G m s.t. ⎧ δ Ii ,, Jj ,,kK, l, L ∈

* C max

−

i , j , k ,l B.β sI , sJ , sK , sL

sI , sJ − t sK , sL

d ki ,,lj

d ki ,,lj

(7) (8)

( i , j , k , l ) ≤ ( I , J , K , L ),

{0,1}

⎪ ⎪ i, j i , j , k ,l i, j I ,J * * ⎨t k ,l − t K , L + C max .δ I , J , K , L ≤ − d k , l + C max ⎪ I ,J i , j , k ,l * I ,J ⎪ t K , L − t ki ,,lj − C ma x .δ I , J , K , L ≤ − d K , L ⎩ * −1 with B ∈ N , B ≥ 2.C max

(9) (10) (11)

Fig. 2 Mixed Integer Programming Model

* • Variable tki ,,lj ∈ cde 0, Cmax − 1fgh corresponds to the activation date of the operation

oki ,,lj within the considered cycle; • Variable δ Ii ,, Jj ,,kK,l, L ∈ {0,1} is the binary variable corresponding to the order between operations performed on the same machine, such that δ Ii,, Jj ,,kK,l, L = 1 if tki ,,lj < tKI ,,JL and 0 otherwise. “Fig.3” presents a scheduling of the illustrative ex1,2,2,2 = 1, since: ample used below (“Fig.6”). In this schedule, we have δ1,2,2,1 1,2 t1,2 2,1 < t2,2 . , k ,l i , j , k ,l • Variables α sIi, j, sJ , sK , sL and β sI , sJ , sK , sL correspond to binary variables used to

compute the WIP: sI , sJ i, j , k ,l -- α sIi , j, sJ , sK , sL = 1 if osK , sL is executed before the completion time of ok ,l , where sI , sJ i, j osK , sL stands for a successor of operation ok ,l in the job; i, j , k ,l -- β sIi , ,jsJ , sK , sL = 1 if ok ,l overlaps two cycles and completes after the activation time sI , sJ of osK , sL on the next cycle;

286


Fig. 3 Variable δ (delta)

Fig. 4 Binary variables used to compute the WIP (α and β)

“Fig.4” presents a scheduling of a cyclic linear job. This job consists of 3 tasks: 1,1 1,1 o1,1 0,1 , o0,2 and o0,3 : 1,1 1,1 1,1 1,1 1,1 o1,1 0,1 is followed by o0,2 , o0,2 is followed by o0,3 and o0,3 is followed by o0,1 .

We presents in “Fig.4” a scheduling to illustrate the case when we have , k ,l = 1 and β sIi , ,jsJ , sK , sL = 1 .

i , j , k ,l α sI , sJ , sK , sL

More explanations for α and β can be found in [2], since these two variables keep the same meaning for systems with or without assembly/disassembly tasks. , k ,l • B ∈ N is a constant used to constrain the discrimination variables α sIi, j, sJ , sK , sL , k ,l and β sIi, ,jsJ , sK , sL in a linear way. It has to be “big enough” (lower bound: * 2.Cmax − 1 ) in order to make the inequalities (5) to (8) valid. This lower bound

was computed as follow:


In tki ,,lj

order sI , sJ − tsK , sL

to

consider

“(6)”

i , j , k ,l − B.α sI , sJ , sK , sL

as a valid inequality, we must have: , k ,l and if we consider α sIi, j, sJ , sK , sL = 1, then:

− d ki ,,lj . ,

≤

287

i, j i, j i, j sI , sJ * * tki ,,lj − tsK , sL + d k ,l ≤ B . In addition, we know that tk ,l ≤ Cmax − 1 and d k ,l ≤ Cmax , then

B must respect the following inequality: * 2.Cmax −1 ≤ B

• Remaining inequalities (5) to (8), (10) and (11) constrain the previous variables according to their meanings. • Finally, the objective function “(1),” corresponds to the minimization of the WIP of the considered scheduling. It consists of two parts: a constant plus decision variables (α and β). Note that, if we consider only decision variables in the objective function (1), the mathematical model will compute, only, the WIP needed for one path and the extra WIP required by the other branches. Hence, to know the WIP of the schedule, we have to add the WIP needed to perform the rest of the branches. Indeed, in “Fig.5” we notice that, after a disassembly task, the system generates (nb–1) new WIP, nb stands for the number of branches in the second stage (Stage_2). For example, before firing transition t1, the system presents one WIP, then, after firing t1, the system presents 3 WIP, which means that we need 2 = (3 –1) extra WIP to process the rest of branches in the second stage. l

m

o n

q

r

¬

s

p

¯

i

¯

i

Fig. 5 Variations of the Numbers of Tokens

In addition to this mathematical model, we define two other properties. Firstly, we consider that the first operation of the first job (operation o1,1 0,1 ) starts at time 0 1,1 (which means that t0,1 = 0 ). Indeed, the steady state can be observed at different

dates and always presents the same WIP. This is due to the cyclic behavior of the production. Hence, generality is maintained by considering that the cycle begins when the execution of operation o1,1 0,1 starts. Secondly, the total WIP is made of the WIP needed to achieve each job separately. Let Ti be the total duration of the ith possible path from the first operation to the last one. If Ti is great to CT, then this sequence of operations is longer than a cycle and has to be cut into several cycles. This is done by introducing several parts of this sequence of operations: WIP. This number has to be at least equal to the integer superior or equal to Ti by CT. WIPmin =

⎡ Ti ⎤ ⎢ ⎥ i: Possible operations sequences ⎢ CT ⎥

∑

(12)

288


Concerning the optimality of the solutions, this model reflects exactly the constraints that can be found in a scheduling problem, namely the constraints of precedence between operations and the constraints of resource sharing. Therefore, this model ensures the optimality of the solutions. On the other hand, we work with an exact approach and the resolution is done by a linear program solver (CPLEX). Note that the mathematical model can deal, either, with problems with linear jobs [2] or with Assembly/Disassembly tasks.

4 Illustrative Example In this section we will use the example “Fig.1” of Disassembly/Assembly system, in order to illustrate the approach to compute optimal WIP with the mathematical model. The original example “Fig.6” was used by Trouillet in [20]. There are two main differences between “Fig.1” and “Fig.6”: • Transition t7 in “Fig.6” will be considered as the first operation in “Fig.1.” In fact, this is possible since the problem is cyclic. • In “Fig.6,” all the transitions are fired once except t1 and t2 which are fired twice. This property is replaced by the use of two successive operations for each transitions t1 and t2. Indeed, this choice is justified by the fact that we use the same resource M3 for these two transitions. Hence, necessarily, transitions t1 and t2 will be performed on M3 sequentially. Here, we look to work with ordinary Petri net for reasons of understanding and readability for our model. The system contains 3 stages. The second stage contains 2 branches.

p1

p2 M3

t1

(3)

t2

(3)

p3 (1)

¾

p4 M5

t3

(1)

¾

p5

t4 p6

(3)

t5

M2

p7 (1)

t6

M4

p8 (1)

t7

Fig. 6 Illustrative example used by Trouillet in [20]

M1


289

There are five resources denoted by M1, M2, M3, M4, M5. The Cycle Time (CT) is equal to 12, which is the workload of M3 (bottleneck resource). To compute a lower bound for the WIP, we know the optimal cycle time CT and the total duration of each possible path from the first task to the last one, through the different branches. For our example, we have two paths: 1,2 1,2 1,2 1,3 1,3 • o1,1 0,1 , o1,1 , o1,2 , o1,3 , o0,1 , o0,3 . 1,2 1,2 1,2 1,3 1,3 • o1,1 0,1 , o2,1 , o2,2 , o2,3 , o0,1 , o0,3 .

If we suppose that we will process only the first path, then we will need at least 12 t.u., which means, at least, one part, i.e. one WIP. Then, the second path needs at least one WIP, as well. ⎡ 12 ⎤ ⎡ 12 ⎤ The WIP lower bound is equal to: ⎢ ⎥ + ⎢ ⎥ = 2 . ⎢ 12 ⎥ ⎢ 12 ⎥

Fig. 7 Scheduling on resources

“Fig.7” represents the computed schedule of tasks on the resources using linear program solver CPLEX 9.0 on an Intel Pentium 4 at 2.8 GHz and 1Go RAM, under Windows XP. The resolution takes about 1s. “Fig.8” represents the same schedule, but, here, we focus on the number of pallets used in the system. “Fig.8” shows that the schedule requires 3 pallets. Hence the optimal number of WIP is equal to 3. This level of WIP was found by the mathematical model through variables α and β:

290


Fig. 8 Scheduling from the part’s point of view 1,1,0,1 1,1,0,1 1,2,1,1 1,2,1,2 1,2,2,1 1,2,2,2 1,2,2,3 1,2,1,3 α1,2,1,1 + α1,2,2,1 + α1,2,1,2 + α1,2,1,3 + α1,2,2,2 + α1,2,2,3 + α1,3,0,1 + α1,3,0,1 + 1,3,0,1 1,3,0,2 1,1,0,1 1,1,0,1 1,2,1,1 1,2,1,2 1,2,2,1 1,2,2,2 α1,3,0,2 + α1,1,0,1 + β1,2,1,1 + β1,2,2,1 + β1,2,1,2 + β1,2,1,3 + β1,2,2,2 + β1,2,2,3 + 1,2,2,3 1,2,1,3 1,3,0,1 1,3,0,2 β1,3,0,1 + β1,3,0,1 + β1,3,0,2 + β1,1,0,1 =2 1,2,1,2 1,3,0,2 All the variables here are null except: α1,2,1,3 = α1,1,0,1 = 1. We can verify these 1,2 1,2 1,2 1,3 1,3 1,1 two values from “Fig.8,” while t1,2 + d1,2 > t1,3 and t0,2 + d 0,2 > t0,1 .

The mathematical approach computes the WIP needed for one path and the extra WIP required by the other branches. Hence, to find out the WIP needed for the whole schedule, we must add (nb–1) pallets (Sect.3.3) to the WIP level found by the resolution of the mathematical model. In this case, the WIP computed using mathematical model is equal to 2 and we have two branches in the second stage. Hence, the WIP of the schedule is equal to 2 + (2 – 1) = 3. We notice here that the optimal WIP computed with our approach is equal to 3 and that the lower bound of the WIP is equal to 2. In fact, this theoretical value cannot be reached. Indeed, we mentioned that we have two possible paths from the first task to the last one. If we consider that we will perform each path separately, which means that we consider that machine M3 will be available at any time. With this relaxation, we need 12 t.u. to perform each path apart, which means 2 WIP. However, “Fig.1” shows that M3 is shared by the two paths. Hence, there will be, necessarily, an extra time while processing one of these two paths, which means that there will be a need for at least one more WIP. Then, the level of WIP found by our approach (3) is thus optimal.

5 Conclusion This paper deals with cyclic scheduling problems with assembly/disassembly tasks and Work-In-Process minimization. The main contribution here is to propose a mathematical model of the scheduling issue of such systems. First, we have presented systems with assembly/disassembly tasks and we have shown the interest of using cyclic scheduling approach to solve these problems. Secondly, we have clearly defined the concept of WIP in these systems.


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Afterwards, we have proposed a mathematical model which deals with the specificity of assembly systems, i.e. synchronization of multiple tasks. Then, we have used an illustrative example that has been previously used by Trouillet [20] to explain our model and our resolution method. This study shows that one can solve optimally problems with assembly/disassembly tasks. We have shown that we can find an optimal scheduling (cycle time) for assembly/disassembly systems like Fournier in [9]. However, our approach allows, in addition, to find the optimal WIP in the system. Future works will consider extended assembly/disassembly systems: with several tasks and imbricated stages. In addition, we can add extra constraints to the problems like working with a limited WIP. Moreover, we aim to substitute the CPLEX solver for an algorithm especially fitted to the mathematical model, in order to improve the resolution time.

References [1] Bellmann, R.: Dynamic Programming. Princeton University Press, Princeton (1965) [2] Ben Amar, M.A., Bourdeaud’huy, T., Korbaa, O.: Cyclic Scheduling MIP Implementation: Cutting Tetchniques. In: ICPR 2007, Valparaiso, Chili (2007) [3] Bourdeaud’huy, T., Korbaa, O.: A Mathematical Model For Cyclic Scheduling With Work-In-Progress Minimization. In: INCOM 2006, Saint Etienne, France (2006) [4] Camus, H., Ohl, H., Korbaa, O., Gentina, J.-C.: Cyclic Schedules in Flexible Manufacturing Systems with Flexibilities in operating sequences. In: Proceedings of the 17th International Conference on Application and Theory of Petri Nets (ICATPN), Osaka, Japan, pp. 97–116 (1996) [5] Chretienne, P., Coffman, E.G., Lenstra, J.K., Liu, Z.: Scheduling: Theory and its applications, ch. 3, pp. 33–64. John Wiley & Sons, Chichester (1997) [6] Driss, O.B., Korbaa, O., Ghedira, K., Yim, P.: A distributed transient inter-production scheduling for flexible manufacturing systems. Journal Europeen des Systemes Automatises, JESA 2007 41(1) (2007) [7] Dupas, R., Cavory, G., Goncalves, G.: Optimising the throughput of a manufacturing production line using a genetic algorithm. In: Real-World Applications GECCO 1999, p. 1775 (1999) [8] Field, F.R., Clark, J.P.: Recycling of USA automobile materials: a conundrum for advanced materials. ATA 1991 44(8/9), 541–555 (1991) [9] Fournier, O., Lopez, P., Lan Sun Luk J.D.: Cyclic scheduling following the social behavior of ant colonies. In: Proceedings of the IEEE International Conference on Systems, Man and Cybernetics 2002, vol. 3, pp. 450–454 (2002) [10] Gupta, S.M., McLean, C.R.: Disassembly of products. Computers and Industrial Engineering 31(1-2), 225–228 (1996) [11] Hanen, C., Munier Kordon, A.: Periodic schedules for linear precedence constraints. Discrete Applied Mathematics 157(2), 280–291 (2009) [12] Hsu, T., Korbaa, O., Dupas, R., Goncalves, G.: Cyclic scheduling for F.M.S.: Modelling and evolutionary solving approach. European Journal of Operational Research, EJOR 191(2), 463–483 (2008) [13] Mo, J., Zhang, Q., Gadh, R.: Virtual Disassembly. International Journal of CAD/CAM 2(1), 29–37 (2002)

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[14] Korbaa, O., Camus, H., Gentina, J.-C.: A New Cyclic Scheduling Algorithm for Flexible Manufacturing Systems. International Journal of Flexible Manufacturing Systems (IJFMS) 14(2), 173–187 (2002) [15] Lambert, A.J.D.: Disassembly sequencing: a survey. International Journal of Production Research 41, 3721–3759 (2003) [16] Mane, A., Nahavandi, S., Zhang, J.: Sequencing production on an assembly line using goal chasing and user defined algorithm. In: Winter Simulation Conference (WSC 2002), vol. 2, pp. 1269–1273 (2002) [17] Mascle, C., Balasoiu, B.A.: Disassembly-assembly sequencing using feature-based life-cycle model. In: Proceedings of 2001 IEEE International Symposium on Assembly and Task Planning, pp. 31–36 (2001) [18] Sundaram, S., Remmler, I., Amato, N.M.: Disassembly sequencing using a motion planning approach. In: Proceedings of 2001 IEEE International Conference on Robotics and Automation, pp. 1475–1480 (2001) [19] Trouillet, B., Benasser, A., Gentina, J.-C.: Transformation of the Cyclic Scheduling Problem of a Large Class of FMS into the Search of an Optimized Initial Marking of a Linearizable Weighted T-System. In: Sixth International Workshop on Discrete Event Systems (WODES 2002), p. 83 (2002) [20] Trouillet, B., Dupas, R., Goncalves, G., Hsu, T.: Two approaches to the cyclic scheduling with assembly. In: 12th IFAC Symposium on Information Control Problems in Manufacturing, INCOM 2006, Saint-Etienne, France (2006) [21] Trouillet, B., Korbaa, O., Gentina, J.-C.: Formal Approach for FMS Cyclic Scheduling. IEEE SMC Transactions, Part C 37(1), 126–137 (2007)

Author Index

Aiyama, Yasumichi

21

Baek, KyeongKeun 141 Baptiste, Pierre 157 Bargiel, Sylwester 99 Bautista, Joaqu´ın 211 Ben Amar, Mohamed Amin Camus, Hervé 279 Chica, Manuel 211 Choi, Byung-Wook 185 Choi, Kyung-Hyun 187 Clécy, Cédric 99 ´ Cord´ on, Oscar 211 Craiovan, D. 113 Damas, Sergio Franke, J.

Gorecki, Christophe

99

Hasegawa, Yuji 35 Heikkil¨ a, Riku 127 Heikkil¨ a, Tapio 171 Hoshino, Satoshi 265 Hwang, Cheol-woong 227 H¨ usig, Matthias 253

J¨ arvenp¨ aa ¨, Eeva Jeong, Seon Hwa

279 Latremouille-Viau, Julie Lee, Eon 227 Lee, Sukhan 97, 141 Lutz, Philippe 99

157

Maeda, Yusuke 85 Maida, Kazuhiro 35 Mascle, Christian 157

211

113

Inui, Masatomo

Kim, Gun Yeon 227 Kim, Hyeonnam 227 Korbaa, Ouajdi 279 Koskinen, Jukka 171 Kubota, Toru 21 Kyung, Jin-Ho 5

35 127 227

Kim, Daesik 141 Kim, Dong-Soo 187

Naka, Yuji 265 Neugebauer, Reimund Noh, Sang Do 227

239

Oh, Jong-Kyu 141 Ota, Jun 265 Park, Chanhun 5 Park, Dong IL 5 Park, Kyoungtaik 5 Park, Yang Ho 227 Penalba, Francesc 53 Pulkkinen, Topi 171 Rabenorosoa, Kanty 99 Roa, M´ aximo A. 69 Rosell, Jan 53

294 Seki, Hiroya 265 Shin, Hyunshik 227 Sterzing, Andreas 239 Su, Yang Bong 187 Su´ arez, Ra´ ul 1, 53, 69

Author Index Thanh, Tran Trung Tuokko, Reijo 127 Ushioda, Tatsuya Youn, Sangil

227

187

85

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