A Cooperative Pursuit-Evasion Game for Non-Holonomic Systems

This paper considers a pursuit-evasion game for non-holonomic systems where a number of pursuers attempt to capture a single evader in a bounded connected domain. The problem is challenging because all vehicles have the same manoeuvring capability and are subject to turn radius constraints making them non-holonomic systems. The paper initially presents simple and alternate proofs for results existing in the literature that guarantee capture for holonomic systems. These results that are based on the minimization of safe-reachable area (the set of points where an evader can travel without being caught) are then extended to non-holonomic systems. However, solving such a problem exactly is computationally intractable. Therefore, the paper proposes a computationally efficient algorithm to obtain an approximate solution to the safe-reachable area minimization problem where the pursuers aim to minimize the safe-reachable area of the evader, while the evader chooses control actions to maximize it. Also proposed is an alternative approach that uses a cooperative strategy based on a pure proportional navigation law to capture the evader. In the process, an evader strategy which is superior to those based on the minimization of safe-reachable area is identified. The paper evaluates the proposed algorithms through numerical simulations.