A Two-Pursuer One-Evader Game with Equal Speed and Finite Capture Radius

In this paper, a two-pursuer one-evader game in the plane is considered. All the agents have simple motion and the same speed. As opposed to the game with superior pursuers, capture can occur in finite time only by defining a nonzero capture radius and for a subset of initial game states. Such a set is characterized and the full game solution is provided. In particular, the value function of the game and explicit expressions of the closed-loop optimal strategies of all the agents are derived. The results are validated via numerical simulations, comparing the optimal control actions with alternative strategies for both the evader and the pursuers.