Reach-avoid games with two heterogeneous defenders and one attacker

This article addresses a reach-avoid game with two heterogeneous defenders and one attacker in a bounded, convex domain consisting of a target region and a play region. The attacker aims to reach the target region before being captured by any defenders, while the defenders strive to capture the attacker in advance. A simple geometric method is introduced that only considers the position relation between the reaching regions of the players and the boundary of the target region to construct the barrier of the two-player version reach-avoid game analytically. Next, based on the speed ratio between the defenders, the necessary and sufficient conditions suitable for the general game setups to judge which defender contributes to the barrier and decompose the problem into several two-player version subproblems are given. Then, the barrier of the original game is constructed analytically by combining these subproblems in all possible situations. The method provided an analytical expression of the barrier and has essentially no computation burden. Thus, the method is suitable for online applications. And solutions given in this work can be extended to general multiplayer situations and the game with complex setups for further research.