Optimal Motion Planning for Differential Drive Mobile Robots based on Multiple-Interval Chebyshev Pseudospectral Methods
Optimal Motion Planning for Differential Drive Mobile Robots based on Multiple-Interval Chebyshev Pseudospectral Methods
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DOI：
10.1017/s0263574720000430
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发表时间：
2020-05
期刊：
影响因子：
2.7
通讯作者：
R. Mao;Hongli Gao;Liang Guo
中科院分区：
文献类型：
--
作者：
R. Mao;Hongli Gao;Liang Guo
本文提出了一种求解具有运动学和动力学约束的非完整移动机器人运动规划问题的切比雪夫伪谱方法。状态变量和控制变量在N阶切比雪夫多项式中展开，并提供切比雪夫-高斯-洛巴托(CGL)节点来逼近系统动力学、边界条件和性能指标。针对障碍物附近节点不足的情况，提出了多区间策略来处理障碍物的越界问题。数值算例表明，多区间策略比单区间切比雪夫PS法具有更高的精度。
SUMMARY 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.