A VISIBILITY-BASED PURSUIT-EVASION PROBLEM

TLDR

The visibility‑based pursuit‑evasion problem was first introduced by Suzuki and Yamashita and is motivated by robotics applications such as mobile‑robot surveillance in cluttered workspaces. This paper addresses the problem of planning the motion of one or more pursuers in a polygonal environment to eventually “see” an evader that is unpredictable, has unknown initial position, and can move arbitrarily fast. The complete algorithm searches a finite graph constructed on the basis of critical information changes. The authors present bounds and a complete algorithm for computing a successful motion strategy for a single pursuer, show that the minimum number of pursuers required is Θ(log n) in simply‑connected free spaces and a specific bound in multiply‑connected spaces, identify problems solvable by one pursuer with linear recontaminations, and demonstrate implementation with computed examples.

Abstract

This paper addresses the problem of planning the motion of one or more pursuers in a polygonal environment to eventually "see" an evader that is unpredictable, has unknown initial position, and is capable of moving arbitrarily fast. This problem was first introduced by Suzuki and Yamashita. Our study of this problem is motivated in part by robotics applications, such as surveillance with a mobile robot equipped with a camera that must find a moving target in a cluttered workspace. A few bounds are introduced, and a complete algorithm is presented for computing a successful motion strategy for a single pursuer. For simply-connected free spaces, it is shown that the minimum number of pursuers required is Θ( lg n). For multiply-connected free spaces, the bound is [Formula: see text] pursuers for a polygon that has n edges and h holes. A set of problems that are solvable by a single pursuer and require a linear number of recontaminations is shown. The complete algorithm searches a finite graph that is constructed on the basis of critical information changes. It has been implemented and computed examples are shown.