Perimeter-defense Game between Aerial Defender and Ground Intruder

TL;DR

This paper extends perimeter-defense pursuit-evasion game analysis from a circular defender to a hemispherical one, deriving optimal strategies, barriers, and Nash equilibrium solutions through theoretical analysis and simulations.

Contribution

It introduces a novel analysis of the perimeter-defense game with a hemispherical defender, including optimal strategies, barrier surfaces, and equilibrium conditions.

Findings

Derived the barrier surface dividing winning regions.

Proved optimal strategies involve moving towards the optimal breaching point.

Validated the strategies as a Nash equilibrium through simulations.

Abstract

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.