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

Abstract

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.

Navigating free‐floating minefields via time‐varying Voronoi graphs

“…For the FFMs we study, perhaps the most closely applicable networks are the Zermelo‐Voronoi diagrams (ZVD) introduced by Bakolas and Tsiotras and very recently employed by Sun and Tsiotras . Unlike a normal Voronoi diagram, a ZVD assumes that its generating points are under the influence of drift.…”

“…Unlike a normal Voronoi diagram, a ZVD assumes that its generating points are under the influence of drift. Like many other applications of Voronoi diagrams generated around moving points , however, Sun and Tsiotras consider the moving points as agents and are primarily concerned with the partitions the ZVD provides as a way to decide which agent should pursue a given target. In contrast, we are interested in the edges that define the diagram as a means to construct a network within which possible ship paths can be identified that maximize the minimum distance to mines.…”

Capturing an Evader Using Multiple Pursuers with Sensing Limitations in Convex Environment

“…In this form of the game, multiple pursuers try to capture a single evader whereas the evader may win by exiting safely from the game region. A number of applications of this variant can be found in security and military applications [4][5][6] . Studied this variant of the pursuitevasion game in the present study.…”

“…The continuous version of the game has been reported in the literature using model predictive control 11,12 , optimisation techniques 13,14 , fuzzy logic and neural network based learning approaches 13,15 . Other recently introduced methods are based on the concept of minimising the evader's Voronoi region for obtaining fast and feasible solutions in pursuit-evasion 6,16 . Sun & Tsiotras 6 have provided a pursuers' strategy based on the dynamic assignment of the pursuers.…”

“…Other recently introduced methods are based on the concept of minimising the evader's Voronoi region for obtaining fast and feasible solutions in pursuit-evasion 6,16 . Sun & Tsiotras 6 have provided a pursuers' strategy based on the dynamic assignment of the pursuers. In this strategy, the working environment is partitioned into Voronoi-like regions which are called the Zermelo-Voronoi Partitions (ZVP).…”