Multiplayer reach-avoid games via low dimensional solutions and maximum matching

We consider a multiplayer reach-avoid game with an equal number of attackers and defenders moving with simple dynamics on a two-dimensional domain possibly with obstacles. The attacking team attempts to send as many attackers to a certain target location as possible quickly while the defenders aim to capture the attackers to prevent the attacking team from reaching its goal. The analysis of problems like this plays an important role in collision avoidance, motion planning, and aircraft control, among other applications. Computing optimal solutions for such multiplayer games is intractable due to numerical intractibility. This paper provides a first attempt to address such computational intractability by combining maximum matching in graph theory with the classical Hamilton-Jacobi-Isaacs approach. In addition, our solution provides an initial step to take cooperation into account by computing maximum matching in real time.