轨迹优化的LASSO网格自适应加密方法

针对轨迹优化直接方法,提出了以控制变量曲率为基础的最小绝对收缩与选择算子(least absolute shrinkage and selection operator,LASSO)网格自适应加密策略,用于提高优化精度。以高分辨率二分网格节点为中心,构造径向基函数逼近控制曲线,利用LASSO方法估计径向基函数系数,并自动筛选出位于控制曲线曲率极大区间的高分辨率节点加密当前网格。本文方法不需要进行状态和控制误差估计,适应性和通用性强。两组典型算例验证了方法的有效性。

LASSO-based node adaptive refinement in trajectory optimization

A least absolute shrinkage and selection operator (LASSO) based node adaptive refinement approach for the direct method in trajectory optimization is proposed. Firstly, a higher resolution grid and its associated radial basis function set are created. Sequentially, the control variables are approximated using the resulting radial basis function set, and its sampling sequence is generated by interpolation. Finally, the coefficients of the formulated approximation function are estimated based on the statistical variable selection method-LASSO. The higher multi-resolution nodes associated with radial basis functions with non-zero coefficient are selected as new nodes. The proposed method refines the mesh without estimation of states and/or errors controls, and few extra parameters are involved. Therefore, the formulated trajectory optimization algorithm behaves strong adaptability and generality. The validity of this method is demonstrated by several typical examples.