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Optimal Motion Planning for Differential Drive Mobile Robots based on Multiple-Interval Chebyshev Pseudospectral Methods

Published online by Cambridge University Press:  29 May 2020

Run Mao ,
Hongli Gao Open the ORCID record for Hongli Gao [Opens in a new window]  and
Liang Guo
Run Mao
Affiliation:
Department of Electromechanical Measuring and Controlling, School of Mechanical Engineering, Southwest Jiaotong University, 610036 Chengdu, Sichuan, People’s Republic of China.
Hongli Gao*
Affiliation:
Department of Electromechanical Measuring and Controlling, School of Mechanical Engineering, Southwest Jiaotong University, 610036 Chengdu, Sichuan, People’s Republic of China.
Liang Guo
Affiliation:
Department of Electromechanical Measuring and Controlling, School of Mechanical Engineering, Southwest Jiaotong University, 610036 Chengdu, Sichuan, People’s Republic of China.
*
*Corresponding author. E-mail: hongli_gao@swjtu.edu.cn
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Summary

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This paper presents a Chebyshev Pseudospectral (PS) method for solving the motion planning problem of nonholonomic mobile robots with kinematic and dynamic constraints. The state and control variables are expanded in the Chebyshev polynomial of order N, and Chebyshev–Gauss–Lobatto (CGL) nodes are provided for approximating the system dynamics, boundary conditions, and performance index. For the lack of enough nodes nearby the obstacles, the interpolation of trajectory may violate the obstacles and the multiple-interval strategy is proposed to deal with the violation. Numerical examples demonstrate that multiple-interval strategy yields more accurate results than the single-interval Chebyshev PS method.

Keywords

Chebyshev pseudospectralMotion planningObstacle avoidanceCGLNonholonomic

Information

Type
Articles
Information
Robotica , Volume 39 , Issue 3 , March 2021 , pp. 391 - 410
Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press

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