A differential game for cooperative target defense

Multi-player pursuit–evasion games are crucial for addressing the maneuver decision problem arising in the cooperative control of multi-agent systems. This work addresses a particular pursuit–evasion game with three players, Target, Attacker, and Defender. The Attacker aims to capture the Target, while avoiding being captured by the Defender and the Defender tries to defend the Target from being captured by the Attacker, while trying to capture the Attacker at an opportune moment. A two-pronged pursuit–evasion problem in this game is considered and we focus on two aspects: the cooperation between the Target and Defender and balancing the roles of the Attacker between pursuer and evader. A barrier based on the explicit policy method and geometric analysis method is constructed to separate the whole state space into two disjoint parts that correspond to two winning regions for the Attacker and Target–Defender team. The main contributions of this work are obtaining the players’ winning regions and providing a complete game solution by analyzing the optimal strategies and trajectories of the players based on the barrier.