Relay Pursuit of an Evader by a Heterogeneous Group of Pursuers using Potential Games

In this paper, we propose a decentralized game-theoretic pursuit policy for a heterogeneous group of pursuers who individually attempt to, without any prescribed cooperative pursuit strategy, capture a single evader who strives to delay or avoid capture if possible. We assume that the pursuers are rational (self-interested) agents who are not necessarily connected via communication network. Our proposed pursuit policy is motivated from the semi-cooperative pursuit policy called relay pursuit [1] under which only the pursuer who can capture the evader faster than the others is active while the rest stay put. In contrast to the latter strategy, our proposed method does not rely on geometric tools. It relies instead on reducing the noncooperative pursuit-evasion game into a sequence of maximum weighted bipartite matching problems which seek to find the pursuer-evader assignments which will result in minimum time of capture. To find the optimal assignment in a decentralized manner, the graph matching problem at each time instant is formulated as a static potential game whose pure strategy Nash equilibria correspond to the optimal assignments. Such equilibria are found by iteratively executing a game-theoretic learning algorithm called Joint Strategy Fictitious Play (JSFP) under which every pursuer synchronously takes his best reply strategy (pursue or stay put), depending on the joint actions of other pursuers, until they reach a Nash equilibrium. We illustrate the performance of our method by means of extensive numerical simulations.