Reach-avoid game with circular goal region

Abstract

This paper studies a reach-avoid game between two adversarial players called attacker and defender. The attacker aims to intrude a circular goal region, while the defender strives to protect the goal region by intercepting the attacker before it reaches the goal region's perimeter. Specifically, the goal region has a disproportionate impact on the two sides, because the defender can't move inside the circular goal region, which means it is an obstacle for the defender. A geometric method is used to construct the barrier of the game so winning regions are determined for the two players. Then a feasible feedback defense strategy is designed for the defender when the initial state is in the defender's winning region to guarantee the attacker been captured before intruding the goal region. Simulation results are presented to validate our methods.