Reach-Avoid Differential Games via Finite-Time Heading Tracking

This paper considers a one-defender-one-attacker reach-avoid differential game (DG) in the plane which is split by a straight line into a goal region and a play region. The attacker aims at entering the goal region from the play region without being captured, while the defender tries to capture the attacker in the play region. We focus on the defense problem where the defender is a Dubins car with non-zero capture radius and the attacker is a simple-motion model. First, a controller is proposed for the defender to track a heading reference which is derived from an evasion space (ES)-based defense strategy. Then, the upper bounds for the time derivative of the heading reference are computed. Based on it, we show that the defender can succeed to track the heading reference within a finite time. Finally, both simulation and experiment examples are provided, where a vision-based re-localization method is used for the experiment to deal with the coordinate inconsistency problem.