Pursuit, evasion and defense in the plane

Multi-player games are important for analyzing complex real-world applications that involve both cooperative and adversarial agents, but computational complexity complicates solving such games. We study a modified pursuit-evasion game with multiple pursuers and a single evader, played in a convex domain with an exit through which the evader may escape. We present a strategy whereby one pursuer acts as a defender, utilizing a multi-mode switching strategy to prevent the evader from escaping while the other pursuers subsequently capture the evader. The strategy requires each pursuer to have knowledge only of its Voronoi neighbors and the evader, and runs in real time. The existence and uniqueness of the players' trajectories are proved using non-smooth analysis, and it is also shown that the evader can never reach the exit regardless of its control inputs, resulting in eventual capture. Simulation results are presented demonstrating the algorithm.