Analytical Solution for Escape Region in Coplanar Spacecraft Pursuit- Evasion Game

The analytical solution of capture and escape regions is a key branch of pursuit-evasion game problem research. Barrier, as the boundary between the capture region and the escape region, has a good property of dividing the state space into the capture region and the escape region. This article proposes a geometric analysis method of “limiting displacement circle”, it establishes the corresponding relationship between the initial state and the final result of the game, decouples the game trajectory from the control strategy, and obtains the analytical solution algorithm for the barrier and escape region. That is, the analytic relationship expressed by the initial orbit radius ratio, thrust acceleration ratio and energy constraints. Finally, the effectiveness of the proposed analytical algorithm was verified through the quantitative differential game algorithm. The proposed analytic solution algorithm directly establishes the relationship between the capture region and the initial state of the game from the theoretical point of view, and can quickly guide the game and provide decision support for the game from the application point of view.

I. Introduction

The two spacecraft orbit pursuit-evasion game problem usually refers to the process of optimal orbit control between a pursuing spacecraft and an escaping spacecraft in a given initial orbit state to achieve a certain adversarial goal [1]–[6]. In the orbit pursuit-evasion game, the capture region indicates that the pursuing spacecraft can capture the escaping spacecraft regardless of the strategy adopted by the escaping spacecraft in this region. The escape region represents a region in which the escaping spacecraft can always find a suitable strategy to avoid the capture of the pursuing spacecraft [7]. The solution of the capture region and escape region depends on qualitative differential games. Qualitative differential games [8]–[15], as a branch of differential games, focus on whether a certain outcome of the game can be achieved: in the case where both pursuers and evaders adopt the optimal strategy, the game outcomes corresponding to different initial states are in the capture region, escape region, or neutral situation (the boundary between capture region and escape region)-the barrier [7]. Therefore, the barrier has the good property of directly establishing the mapping relationship between the initial state and the terminal state of the game and has the boundary of application. Based on the barrier, the analytical existence form of the escape region or capture region can be further solved.