Multiple Equal-Speed Players in Reach-Avoid Differential Games: Non-point Capture

This paper investigates multi-player reach-avoid differential games with non-point capture scenarios. The objective of the attackers’ team is to reach a specific edge of the game boundary, while the defenders’ team aims to capture as many attackers as possible to prevent them from reaching the target line. First, utilizing geometric methods, particularly hyperbolas, we partition the state space into the defensive advantage region and the offensive advantage region, obtaining analytical forms of the barriers. Next, we propose optimal analytical strategies under different payoff functions for equal-speed players whose initial states fall within distinct dominant regions. Furthermore, we provide defenders with an efficient task assignment algorithm that facilitates swift matching of corresponding attackers, significantly reducing the computational burden.