Perimeter-defense Game between Aerial Defender and Ground Intruder
This work extends the theoretical understanding of pursuit-evasion games for robotic security applications, specifically for scenarios involving aerial defenders and ground intruders.
This paper analyzes a perimeter-defense game where a ground intruder attempts to reach the base plane of a hemisphere without being captured by an aerial defender moving on the hemisphere. The study identifies optimal breaching points and strategies for both players, demonstrating that these strategies form a Nash equilibrium.
We study a variant of pursuit-evasion game in the context of perimeter defense. In this problem, the intruder aims to reach the base plane of a hemisphere without being captured by the defender, while the defender tries to capture the intruder. The perimeter-defense game was previously studied under the assumption that the defender moves on a circle. We extend the problem to the case where the defender moves on a hemisphere. To solve this problem, we analyze the strategies based on the breaching point at which the intruder tries to reach the target and predict the goal position, defined as optimal breaching point, that is achieved by the optimal strategies on both players. We provide the barrier that divides the state space into defender-winning and intruder-winning regions and prove that the optimal strategies for both players are to move towards the optimal breaching point. Simulation results are presented to demonstrate that the optimality of the game is given as a Nash equilibrium.