SUMMARYThis 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.

中文翻译：

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基于多区间切比雪夫伪谱法的差分驱动移动机器人最优运动规划

摘要本文提出了一种切比雪夫伪谱（PS）方法，用于解决具有运动学和动态约束的非完整移动机器人的运动规划问题。状态和控制变量在 Chebyshev 阶多项式中展开ñ, 和 Chebyshev-Gauss-Lobatto (CGL) 节点用于近似系统动力学、边界条件和性能指标。由于障碍物附近节点数量不足，轨迹插值可能会违反障碍物，提出了多区间策略来处理。数值示例表明，多区间策略比单区间 Chebyshev PS 方法产生更准确的结果。