Optimal Evading Strategies and Task Allocation in Multi-player Pursuit–Evasion Problems

Abstract

Pursuit–evasion problems involving multiple pursuers and evaders are studied in this paper. The pursuers and the evaders are all assumed to be identical, and the pursuers are assumed to follow either a constant bearing or a pure pursuit strategy, giving rise to two distinct cases. The problem is simplified by adopting a dynamic divide and conquer approach, where at every time instant each evader is assigned to a set of pursuers based on the instantaneous positions of all the players. In this regard, the corresponding multi-pursuer single-evader problem is analyzed first. Assuming that the evader knows the positions of all the pursuers and their pursuit strategy, the time-optimal evading strategies are derived for both constant bearing and pure pursuit cases for the pursuers using tools from optimal control theory. In the case of a constant bearing strategy, and assuming that the evader can follow any strategy, a dynamic task allocation algorithm is proposed for the pursuers. The algorithm is based on the well-known Apollonius circle and allows the pursuers to allocate their resources in an intelligent manner while guaranteeing the capture of the evader in minimum time. For the case of pure pursuit, the algorithm is modified using the counterpart of the Apollonius circle leading to an “Apollonius closed curve.” Finally, the proposed algorithms are extended to assign pursuers in the case of a problem with multiple pursuers and multiple evaders. Numerical simulations are included to demonstrate the performance of the proposed algorithms.