Reach-avoid games for players with damped double integrator dynamics

This paper studies a reach-avoid game of two damped double integrator players. An attacker aims to reach a static target, while a faster defender tries to protect the target by intercepting the attacker before it reaches the target. In scenarios where the defender succeeds, the defender aims to maximize the attacker's final distance from the target, while the attacker aims to minimize it. This work focuses on determining the equilibrium strategy in the defender-winning scenarios. The optimal state feedback strategy is obtained by a differential game approach combining geometric analysis. We construct a multiple reachable region to analyse the damped double integrator player's motion under optimal strategy. Building on this, a new type of the attacker's dominance region is introduced for the first time. It is shown that different strategies are required when the terminal point lies in distinct areas of the attacker's dominance region. Then, a necessary condition is derived for the proposed strategy to be optimal using differential game approach. Furthermore, a case where both players start at rest is discussed, and some useful properties about the dominance region and the optimal strategy are presented. Simulations are conducted to show the effectiveness of the proposed strategy.