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Path constrained time-optimal motion of a cooperative two robot system

Published online by Cambridge University Press:  09 March 2009

Hye-Kyung Cho ,
Bum-Hee Lee  and
Myoung-Sam Ko
Hye-Kyung Cho
Affiliation:
Department of Control and Instrumentation Engineering, Automation and Systems Research Institute, Seoul National University, San 56–1, Shinrim-dong, Kwanak-ku, Seoul 151–742 (Korea)
Bum-Hee Lee
Affiliation:
Department of Control and Instrumentation Engineering, Automation and Systems Research Institute, Seoul National University, San 56–1, Shinrim-dong, Kwanak-ku, Seoul 151–742 (Korea)
Myoung-Sam Ko
Affiliation:
Department of Control and Instrumentation Engineering, Automation and Systems Research Institute, Seoul National University, San 56–1, Shinrim-dong, Kwanak-ku, Seoul 151–742 (Korea)
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Summary

This paper presents a systematic approach to the time-optimal motion planning of a cooperative two robot system along a prescribed path. First, the minimum-time motion planning problem is formulated in a concise form by parameterizing the dynamics of the robot system through a single variable describing the path. The constraints imposed on the input actuator torques and the exerted forces on the object are then converted into those on that variable, which result in the so-called admissible region in the phase plane of the variable. Considering the load distribution problem that is also involved in the motion, we present a systematic method to construct the admissible region by employing the orthogonal projection technique and the theory of multiple objective optimization. Especially, the effects of viscous damping and state-dependent actuator bounds are incorporated into the problem formulation so that the case where the admissible region is not simply connected can be investigated in detail. The resultant time-optimal solution specifies not only the velocity profile, but also the force assigned to each robot at each instant. Physical interpretation on the characteristics of the optimal actuator torques is also included with computer simulation results.

Keywords

Cooperative robotsTime-optimal motionPrescribed pathComputer simulation
Type
Articles
Information
Robotica , Volume 13 , Issue 4 , July 1995 , pp. 363 - 374
Copyright
Copyright © Cambridge University Press 1995

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References

1.Choi, M.H., Ko, M.S. and Lee, B.H., “Optimal Load Distribution for Two Cooperating Robots Using Force Ellipsoid” Robotica 11, 61–72 (1993).CrossRefGoogle Scholar
2.Zheng, Y.F. and Luh, Y.J.S., “Optimal Load Distribution for Two Industrial Robots Handling a Single Object” Trans, of the ASME, J. of Dynamic Systems, Measurement, and Control 111, 232–237 (06, 1989).CrossRefGoogle Scholar
3.Cheng, F.T. and Orin, D.E., “Efficient Algorithm for Optimal Force Distribution – the Compact-Dual LP Method” IEEE Trans. Robotics and Automation 6, No. 2, 178–187 (04., 1990).CrossRefGoogle Scholar
4.Orin, D.E. and Oh, S.Y., “Control of Force Distribution in Robotic Mechanisms Containing Closed Kinematic Chains” Trans, of the ASME, J. of Dynamic Systems, Measurement, and Control 102, 134–141 1981).CrossRefGoogle Scholar
5.Kerr, J. and Roth, B., “Analysis of Multifingered Hands” Int. J. Robotics Research 4, No. 4, 3–17 (1985)CrossRefGoogle Scholar
6.Shin, K.G. and McKay, N.D., “Minimum-Time Control of Robotic Manipulators with Geometric Path Constraints” IEEE Trans. Automatic Control AC-30, No. 6 (06, 1985).Google Scholar
7.Bobrow, J.E., Dubowsky, S. and Gibson, J.S., “Time-Optimal Control of Robotic Manipulators along Specified Paths” Int. J. Robotics Research 4, No. 3, 3–17 (1985).CrossRefGoogle Scholar
8.Pfeiffer, F. and Johanni, R., “A Concept for Manipulator Trajectory Planning” IEEE Trans. Robotics and Automation 3, No. 2,115–123 (04, 1987).Google Scholar
9.Slotine, J.E. and Yang, H.S., “Improving the Efficiency of Time-Optimal Path-Following Algorithms”IEEE Trans. Robotics and Automation 5, 118–124 (1989).CrossRefGoogle Scholar
10.Shiller, Z. and Lu, H., “Robust Computation of Path Constrained Time Optimal Motions” IEEE int. Conf. on Robotics and Automation(1990) pp. 144–149.Google Scholar
11.Chen, Y. and Desrochers, A. A., “Structure of Minimum-Time control Law for Robotic Manipulators with Constrained Paths” IEEE Int. Conf. on Robotics and Automation(1989) pp. 971–976.Google Scholar
12.Ahmad, S. and Yan, H.C., “Minimum-Time Trajectory for Multiple Manipulators Holding a Common Object” Proc. IFAC-AIPAC Conf.,Nancy, France(July, 1989).CrossRefGoogle Scholar
13.Moon, S.B. and Ahmad, S., “Time Optimal Trajectories for Cooperative Multi-Robot Systems,” Proc. of the 29th Conf. on Decison and Control,Honolulu, Hawaii(December, 1990) pp. 1126–1127.CrossRefGoogle Scholar
14.Bobrow, J.E., McCarthy, J.M. and Chu, V.K., “Minimum-Time Trajectories for Two Robots Holding the Same Workpiece,” Proc. of the 29th Conf. on Decision and Control,Honolulu, Hawaii(December, 1990) pp. 3101–3107.CrossRefGoogle Scholar
15.Dudar, A.M. and Eltimsahy, A.H., “A Near-Minimum Time Controller for Two Coordinating Robots Grasping on Object” IEEE Int. Conf. on Robotics and Automation(1990) pp. 1184–1189.Google Scholar
16.Chen, Y., “Existence and Structure of Minimum-Time Control for Multiple Robot Arms Handling a Common Object” Int. J. Control 53, No. 4, 855–869 (1991).CrossRefGoogle Scholar
17.McCarthy, J.M. and Bobrow, J.E., “The Number of Saturated Acutators and Constraint Forces during Time-Optimal Movement of a General Robotic System” IEEE Trans. Robotics and Automation 8, No. 3, 407–409 (06, 1992).CrossRefGoogle Scholar
18.Cho, H.K., Lee, B.H. and Ko, M.S., “Minimum-Time Trajectory Planning for Cooperative Two Robot Arms” Proc. of the 31th SICE Conference,Kumamoto, Japan(July, 1992) pp. 963–966.Google Scholar
19.Moon, S.B. and Ahmad, S., “Sub-Time-Optimal Trajectory Plannings for Cooperative Multi-Manipulator Systems Using the Load Distribution Scheme” IEEE Int. Conf. on Robotics and Automation(1993) pp. 1037–1042.Google Scholar
20.Cho, H.K., Lee, B.H. and Ko, M.S., “Path Constrained Time-Optimal Motion of a Cooperative Two Robot System” IECON'93, Hawaii (1993) pp. 1494–1499.Google Scholar
21.Murty, K.G., Linear Programming (John Wiley & Sons, New York, 1983).Google Scholar