Game Tree Search-based Impulsive Orbital Pursuit–Evasion Game with Limited Actions

This paper focuses on the impulsive orbital pursuit–evasion game (OPEG) with limited action sets for the pursuer and evader. Initially, a mathematical model is developed by combining game theory and orbital dynamics, forming a finite-round impulsive OPEG problem. The problem is then formulated as a bilateral optimization problem, employing a minimum-maximum optimization index based on terminal distance. To tackle this problem, an algorithm based on game tree search is designed, enabling the determination of the optimal pursuit–evasion strategy with limited action sets. Additionally, we explore the influence of the initial pursuing orientation on OPEG. The optimal initial pursuit orientation is analytically derived using relative motion dynamics under uncontrolled conditions. Furthermore, considering factors such as the initial status of the pursuit spacecraft, initial relative distance, transfer time, and maneuverability, the impulsive OPEG problem with limited action sets is numerically solved using game tree search. The findings of this study showcase the efficacy of game tree search in addressing impulsive OPEG problems with limited action sets. The study also demonstrates that the initial pursuing orientation selection at the start of the game plays a crucial role in increasing the success rate of pursuit. The research findings of this study have important implications for future practical engineering applications.