Multiple Pursuer Single Evader Border Defense Differential Game

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. In this paper, we consider 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. We formulate 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 comprised of straight-line segments. This game may contain a dispersal surface which has interesting practical consequences when the optimal strategies are applied in discrete time.

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DOI: 10.2514/1.I010740