Reach-Avoid Games Via Mixed-Integer Second-Order Cone Programming

Joseph Lorenzetti, Mo Chen, Benoit Landry, Marco Pavone

Abstract: Reach-avoid games are excellent proxies for studying many problems in robotics and related fields, with applications including multi-robot systems, human-robot interactions, and safety-critical systems. However, solving reach-avoid games is difficult due to the conflicting and asymmetric goals of agents, and trade-offs between optimality, computational complexity, and solution generality are commonly required. This paper seeks to find attacker strategies in reach-avoid games that reduce computational complexity while retaining solution quality by using a receding horizon strategy. To solve for the open-loop strategy fast enough to enable a receding horizon approach, the problem is formulated as a mixed-integer second-order cone program. This formulation leverages the use of sums-of-squares optimization to provide guarantees that the strategy is robust to all possible defender policies. The method is demonstrated through numerical and hardware experiments.