Reach-avoid games for players with damped double integrator dynamics

Abstract

This paper investigates a reach-avoid game between two players with damped double integrator dynamics. An optimal state-feedback strategy is derived using a differential game framework combined with geometric analysis. To facilitate the analysis, we introduce the concept of multiple reachable region by characterizing the motion of players with damped double integrator dynamics. Based on this, a new type of the attackers dominance region is introduced. We show that distinct strategies are required depending on the location of the terminal position within different areas of the attacker's dominance region. Furthermore, we prove that the proposed strategies satisfy the necessary condition for optimality. Numerical simulations are provided to illustrate the conclusions.