Feedback Strategies for a Reach-Avoid Game With a Single Evader and Multiple Pursuers

We address a planar multiagent pursuit-evasion game with a terminal constraint (reach-avoid game). Specifically, we consider the problem of steering a single evader to a target location, while avoiding capture by multiple pursuers. We propose a feasible control strategy for the evader, against a group of pursuers that adopts a semi-cooperative strategy. First, we characterize a partition of the game's state-space, that allows us to determine the existence of a solution to the game based on the initial conditions of the players. Next, based on the time-derivative of an appropriately defined risk metric, we develop a nonlinear state feedback strategy for the evader which provides a feasible solution to the game. This control strategy involves switching between different control laws in different parts of the state-space. We demonstrate the efficacy of our proposed feedback control in terms of the evader's performance, through numerical simulations. We also show that for the special case of the reach-avoid game with only one pursuer, the proposed control law is successful in guiding the evader to the target location from almost all initial conditions, and ensures that the evader will remain uncaptured.