A cooperative homicidal chauffeur game

We address a pursuit-evasion problem involving an unbounded planar environment, a single evader, and multiple pursuers moving along curves of bounded curvature. The problem amounts to a multi-agent version of the classic homicidal chauffeur problem; we focus on parameter ranges in which a single pursuer is not sufficient to capture the evader. We propose a novel cooperative strategy in which the pursuers move in a daisy-chain formation and confine the evader to a bounded region. The proposed policy is inspired by certain hunting and foraging behaviors of various fish species. We characterize the required number of pursuers and the required value of the evader/pursuers speed ratio for which our strategy is guaranteed to lead to confinement.