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Planning of quasi-minimum time trajectories for robot manipulators (Generation of a bang-bang control)

Published online by Cambridge University Press:  09 March 2009

M. Yamamoto  and
A. Mohri
M. Yamamoto
Affiliation:
Department of Mechanical Engineering, Production Division, Faculty of Engineering, Kyushu University, 6–10–1 Hakozaki Higashiku, Fukuoka 812 (Japan)
A. Mohri
Affiliation:
Department of Mechanical Engineering, Production Division, Faculty of Engineering, Kyushu University, 6–10–1 Hakozaki Higashiku, Fukuoka 812 (Japan)
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Summary

A method for planning minimum time joint trajectories for robot manipulators is discussed. The minimum time trajectory planning problem for manipulators is one of the minimum time control problems of non-linear systems. The optimal input torque/force is of a bang-bang type, except for the singular control derived from the Maximum Principle. An algorithm for generating a bang-bang control is proposed. In the algorithm, the switching time vector is updated to decrease the final state error. The proposed algorithm is applied to a simple manipulator with two links, and the solution by this algorithm is compared with the sub-optimal solution obtained by another approximate method.

Keywords

ManipulatorTrajectory planningMinimum time controlMaximum principleBang-bang control
Type
Research Article
Information
Robotica , Volume 7 , Issue 1 , January 1989 , pp. 43 - 47
Copyright
Copyright © Cambridge University Press 1989

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References

1.Dubowsky, S. and Shiller, Z., “Optimal Dynamic Trajectories for Robotic Manipulators” Procs. of RoManSy, 5th CISM-lFToMM Symp. 133–143 (1984).Google Scholar
2.Shin, K.G. and McKay, N.D., “Minimum-Time Control of Robotic Manipulators with Geometric Path Constraints” IEEE Trans. AC 30, No. 6, 531–541 (1985).CrossRefGoogle Scholar
3.Ozaki, H., Yamamoto, M. and Mohri, A., “Planning of Joint Trajectories of Manipulators with Geometric Path Constraints” Trans. Soc. Instrum. Control. Engrs. 23, No. 3, 288–293 (1987).CrossRefGoogle Scholar
4.Ozaki, H., Yamamoto, M. and Mohri, A. “Planning of Near-Minimum Time Joint Trajectory for Manipulators Using B-spline” Trans. Soc. Instrum. Control Engrs. 23, No. 11, 1199–1205 (1987).CrossRefGoogle Scholar
5.Rajan, V.T., “Minimum Time Trajectory Planning”, Procs. of IEEE Conf. on Robotics and Automation, 759–764 (1985).Google Scholar
6.Dubowsky, S., Norris, M.A. and Shiller, Z., “Time-Optimal Trajectory Planning for Robotic Manipulators with Obstacle Avoidance: A CAD Approach” Procs. of IEEE Conf. on Robotics and Automation, 1906–1912 (1986).Google Scholar
7.Ailon, A. and Langholz, G., “On the Existence of Time-Optimal Control of Mechanical Manipulators” J. Optimization Theory and Applications 46, No. 1, 1–21 (1985).CrossRefGoogle Scholar
8.Kahn, M.E. and Roth, B., “The Near-Minimum-Time Control of Open-Loop Articulated Kinematic Chains” Trans, of the ASME J. Dyn. Sys., Meas, and Control 93, No. 3, 164–172 (1971).Google Scholar
9.Geering, H.P., Guzzella, L., Hepner, S.A.R. and Onder, C.H., “Time-Optimal Motions of Robots in Assembly Tasks” IEEE Trans. AC 31, No. 6, 512–518 (1986).CrossRefGoogle Scholar