A rapid trajectory optimization method based on parallel computing

基于并行计算的轨迹快速优化方法研究

School of Astronautics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Received: 24 August 2024

Abstract

The direct collocation method transforms a trajectory optimization problem into a nonlinear programming (NLP) problem by discretizing both control and state variables. During the NLP solution process, repeated calculations of the first and second derivatives of the NLP and the values of the dynamic system at each discrete point are required, leading to great computational complexities. Therefore, this paper proposes the following method: First, the hyper-dual number method is introduced to accurately identify the sparsity of the second-derivative matrix of the NLP and to determine the locations of the non-zero elements. Then, a multi-core parallel approach is used to rapidly compute the non-zero elements of the first and second derivatives of the NLP as well as the values of the dynamic system at each discrete point. Finally, OpenMP is employed for programming calculation in the C++ environment to further enhance computational efficiency from the perspective of programming language. Simulation results demonstrate that the proposed method effectively improves the efficiency of trajectory optimization and its computational efficiency without compromising accuracy.

摘要

直接配点法通过对控制变量和状态变量都进行离散将轨迹优化问题转化为非线性规划(nonlinear programming, NLP)进行求解。在求解NLP时, 需要反复计算NLP的一阶/二阶偏导数和动力学系统在各离散点处的值, 计算量比较大。针对该问题, 提出如下解决策略: 引入超对偶数方法准确识别NLP二阶偏导数矩阵的稀疏型, 确定其中非零元素的位置; 采用多核并行方式快速计算NLP的一阶/二阶偏导数的非零元素以及动力学系统在各离散点处的值; 在C++环境下采用OpenMP方式进行编程计算, 从编程语言角度进一步提高计算效率。仿真结果表明, 文中方法给出的策略在不影响精度的情况下, 均能显著提高轨迹优化效率。