分析插值误差和斜率的轨迹优化网格细化方法

提出一种基于插值误差和斜率分析的轨迹优化自适应网格细化方法，包括节点插入算法和节点删除算法。节点插入算法分析各个离散节点的控制变量的插值误差。若插值误差较大，则在该节点周围增加节点细化网格；否则，不进行细化。节点删除算法分析各个离散节点处的控制变量斜率。若某个节点的左斜率和右斜率都为零，那么删除该节点；否则，保留该节点。采用三个典型的轨迹优化算例验证了所提出的方法的有效性和特色，并且与其它几种网格细化方法进行了对比。仿真结果表明，本文方法生成的网格规模较小，需要的网格迭代次数较少，能够快速、高精度求解非光滑轨迹优化问题。

Mesh Refinement Method for Trajectory Optimization by Analyzing Interpolation Error and Slope Analysis

An adaptive mesh refinement method for solving the trajectory optimization problem is presented, which consists of the grid point insertion algorithm and the grid point elimination algorithm. The grid point insertion algorithm analyzes the interpolation errors of control variables at each of the grid point, and adds some neighboring grid points if the interpolation errors are large. The grid point elimination algorithm calculates the left and the right slopes of control variables at each of the grid point, and deletes the grid point where both the left and the right slopes are equal to zero. The proposed method is verified by using three typical optimal control problems and compared with several other mesh refinement methods. The numerical results indicate that the proposed method generates significantly smaller mesh size and requires even fewer mesh iterations for a given accuracy when compared with other mesh refinement methods. As a result, the proposed method can solve non-smooth trajectory optimization problems rapidly and accurately.