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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 ,
Xiao-Shan Gao  and
Qiang Zhang
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
*
*Corresponding author. E-mail: xgao@mmrc.iss.ac.cn
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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.

Keywords

Robust trajectory planningRobotic manipulatorsStochastic optimizationProbability constraintLinear programming
Type
Articles
Information
Robotica , Volume 35 , Issue 12 , December 2017 , pp. 2400 - 2417
Copyright
Copyright © Cambridge University Press 2017 

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