Multiplayer reach-avoid differential games with simple motions: A review

This paper reviews the recent works on multiplayer reach-avoid (M-RA) differential games between two adversarial teams in a game region which is split into a goal region and a play region. The pursuit team aims to protect the goal region from the evasion team by cooperatively capturing the evaders which start from the play region and strive to enter the goal region. We provide a selective overview of algorithms and theoretical results for multiplayer reach-avoid differential games. Specifically, we focus on point mass holonomic players that can move freely in the game region and have simple motions as Rufus Isaacs states. We describe how the challenges due to high-dimensional continuous joint action and state spaces, as well as complex cooperations and competitions among players, can be properly resolved by a combination of qualitative and quantitative analysis of small-scale games and optimal task allocation. We finally point out the limitations of the current works and identify fruitful future research directions on theoretical studies of multiplayer reach-avoid differential games.