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.