Relay pursuit of a maneuvering target using dynamic Voronoi diagrams

This paper addresses the problem of the pursuit of a maneuvering target by a group of pursuers distributed in the plane. This pursuit problem is solved by associating it with a Voronoi-like partitioning problem that characterizes the set of initial positions from which the target can be intercepted by a given pursuer faster than any other pursuer from the same group. In the formulation of this partitioning problem, the target does not necessarily travel along prescribed trajectories, as it is typically assumed in the literature, but, instead, it can apply an ''evading'' strategy in an effort to delay or, if possible, escape capture. We characterize an approximate solution to this problem by associating it with a standard Voronoi partitioning problem. Subsequently, we propose a relay pursuit strategy, that is, a special group pursuit scheme such that, at each instant of time, only one pursuer is assigned the task of capturing the maneuvering target. During the course of the relay pursuit, the pursuer-target assignment changes dynamically with time based on the (time varying) proximity relations between the pursuers and the target. This proximity information is encoded in the solution of the Voronoi-like partitioning problem. Simulation results are presented to highlight the theoretical developments.