Orbital Impulsive Pursuit–Evasion Game in the Cislunar Space

A pursuer and an evader can exploit low-energy, non-Keplerian trajectories in cislunar space, making it difficult to obtain the saddle point for impulsive orbital pursuit–evasion games (OPEG). To address this problem, this paper first establishes a zero-sum differential game model based on the circular restricted three-body problem (CR3BP), where the terminal interception time is taken as the performance objective. The necessary optimality conditions for impulsive maneuvers are then derived using Pontryagin’s Maximum Principle (PMP), which transforms the optimal control problem into multipoint boundary value problems (MPBVPs). Subsequently, to overcome the high sensitivity of the MPBVPs to initial costate vectors in shooting methods, a two-layer hybrid initial-guess strategy combining a genetic algorithm with a time-domain coarse-grid search method is proposed for the single-impulse case. Furthermore, a receding-horizon strategy is introduced to generate the initial impulse sequence guess stage by stage for multiple-impulse cases. Finally, numerical simulations demonstrate that the proposed initial-guess strategy can effectively obtain the Stackelberg equilibrium solution for representative cislunar scenarios, including distant retrograde orbits (DROs) and Halo orbits. Meanwhile, the effects of observation delay and three-dimensional orbital characteristics on the game outcomes are also discussed based on dynamic game theory.