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An efficient stochastic approach for robust time-optimal trajectory planning of robotic manipulators under limited actuation

Published online by Cambridge University Press:  03 April 2017

Ming-Yong Zhao
Affiliation:
KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China. E-mails: 1988zmy@gmail.com, automatic_zhangqiang@126.com BKLPUMEC, Department of Mechanical Engineering, Tsinghua University, Beijing, 100084, China
Xiao-Shan Gao
Affiliation:
KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China. E-mails: 1988zmy@gmail.com, automatic_zhangqiang@126.com
Qiang Zhang
Affiliation:
KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China. E-mails: 1988zmy@gmail.com, automatic_zhangqiang@126.com

Summary

This paper focuses on the problem of robust time-optimal trajectory planning of robotic manipulators to track a given path under a probabilistic limited actuation, that is, the probability for the actuation to be limited is no less than a given bound κ. We give a general and practical method to reduce the probabilistic constraints to a set of deterministic constraints and show that the deterministic constraints are equivalent to a set of linear constraints under certain conditions. As a result, the original problem is reduced to a linear optimal control problem which can be solved with linear programming in polynomial time. In the case of κ = 1, the original problem is proved to be equivalent to the linear optimal control problem. Overall, a very general, practical, and efficient algorithm is given to solve the above problem and numerical simulation results are used to show the effectiveness of the method.

Type
Articles
Information
Robotica , Volume 35 , Issue 12 , December 2017 , pp. 2400 - 2417
Copyright
Copyright © Cambridge University Press 2017 

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