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We propose a hybrid approach that combines Hamilton-Jacobi (HJ) reachabilityand mixed-integer optimization for solving a reach-avoid game with multipleattackers and defenders. The reach-avoid game is an important problem withpotential applications in air traffic control and multi-agent motion planning;however, solving this game for many attackers and defenders is intractable dueto the adversarial nature of the agents and the high problem dimensionality. Inthis paper, we first propose an HJ reachability-based method for solving thereach-avoid game in which 2 attackers are playing against 1 defender; we derivethe numerically convergent optimal winning sets for the two sides inenvironments with obstacles. Utilizing this result and previous results for the1 vs. 1 game, we further propose solving the general multi-agent reach-avoidgame by determining the defender assignments that can maximize the number ofattackers captured via a Mixed Integer Program (MIP). Our method generalizesprevious state-of-the-art results and is especially useful when there are fewerdefenders than attackers. We validate our theoretical results in numericalsimulations.

Multi-Agent Reach-Avoid Games: Two Attackers Versus One Defender and Mixed Integer Programming