Optimal Two-Evader Cooperative Strategy Against a Single Pursuer for a 3D Reach-Avoid Game

A reach-avoid problem with two evaders that target a plane in 3D space against a pursuer is studied. In this work, we propose a theorem for the optimal cooperation strategy for two evaders targeting a plane defended by a faster pursuer. This cooperation strategy is tested against two pursuer’s strategies: one that needs the evaders’ control command at the current time – which is unrealistic in adversarial settings – and one that uses only the system state at the current time. We also investigate the latter pursuer’s strategy when the system is implemented in discrete-time with a realistic sampling rate. We do this because the proof is only established for continuous-time. The theoretical results as well as the discrete-time investigations are illustrated by simulations.