Sequential pursuit of multiple targets under external disturbances via Zermelo-Voronoi diagrams.

We address the problem of pursuit between a collection of targets and a team of pursuers distributed in the plane subject to an environmental disturbance (e.g., wind, sea current). The objective of the pursuers is to intercept the moving targets which, however, are not affected by the presence of the flow field. We first solve the multiple-pursuers/single-target problem by assigning only one pursuer to chase the target at every instant of time, based on a Voronoi-like partition of the plane. During the pursuit, the pursuer assignment changes dynamically based on this partition. We then present an algorithm to efficiently update this Voronoi-like partition on-line. The results are then extended to the multiple-pursuers/multiple-targets case. Simulations are included to illustrate the theoretical results.