A path defense approach to the multiplayer reach-avoid game

We consider a multiplayer reach-avoid game played between N attackers and N defenders moving with simple dynamics on a general two-dimensional domain. The attackers attempt to win the game by sending at least M of them (1 ≤ M ≤ N) to a target location while the defenders try to prevent the attackers from doing so by capturing them. The analysis of this game plays an important role in collision avoidance, motion planning, and aircraft control, among other applications involving cooperative agents. The high dimensionality of the game makes computing an optimal solution for either side intractable when N > 1. The solution is difficult even when N = 1. To address this issue, we present an efficient, approximate solution to the 1 vs. 1 problem. We call the approximate solution the “path defense solution”, which is conservative towards the defenders. This serves as a building block for an approximate solution of the multiplayer game. Compared to the classical Hamilton-Jacobi-Isaacs approach for solving the 1 vs. 1 game, our new method is orders of magnitude faster, and scales much better with the number of players.