Application of the hp-adaptive pseudospectral method in spacecraft orbit pursuit-evasion game

Abstract

In this paper, a Cartesian model of the orbit pursuit-evasion game under J2 perturbations is constructed, and a step-by-step solution method applicable to this problem, namely the Hp-Adaptive Pseudospectral Hybrid Optimal Algorithm, is proposed by analyzing the principle of the pseudospectral method and the costate mapping principle. We first use the hp-adaptive Radau pseudospectral method to solve the one-sided interception problem to obtain a tentative guess of the costate and then get the saddle-point solution of the game problem by solving the two-point boundary value problem through the Newton method. The numerical results show that the hybrid method proposed in this work can efficiently find the optimal trajectory of interception and the optimal control laws of the game problem and have high accuracy. In addition, the effects of J2 perturbations and the initial orbital altitude of the evader on the game results and the algorithm itself are discussed in this paper.