Multiple-Pursuer, Single-Evader Border Defense Differential Game

Abstract

Ensuring border security against potential threats has been a long-standing problem, and it becomes much more challenging for international borders due to their massive physical extent coupled with varied terrain. This paper considers a scenario in which a team of UAVs (the pursuers) attempt to prevent an intruder ground vehicle (the evader) from escaping through the border. The ground intruder’s presence is made known by a laser fence positioned inside the border. Upon detection, the UAVs are activated and given the objective to cooperatively capture the intruder. This paper formulates the scenario as a zero-sum differential game whereupon all agents exhibit simple motion and the pursuers have a speed advantage. For cases where capture inside the border is possible, the payoff/cost for the pursuers/evader is the distance from capture to the border. The solution to the game is derived based on the geometric properties of the game and verified for the single-pursuer case with a border comprising straight-line segments. This game may contain a dispersal surface that has interesting practical consequences when the optimal strategies are applied in discrete time.