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. A visibility region is associated with each pursuer, and the goal is to guarantee that the evader will ultimately lie in at least one visibility region. The study of this problem is motivated in part by robotics applications, such as surveillance with a mobile robot equipped with a camera that must nd 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 simply-connected free space, a logarithmic bound is established on the minimum of pursuers needed. Loose bounds for multiply-connected free spaces are also given. 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 nite cell complex that is constructed on the basis of critical information changes. This concept can be applied in principle to multiple-pursuer problems, and the case of a single pursuer has been implemented. Several solution strategies are shown, most of which were computed in a few seconds on a standard workstation.
In a polygonal free space, the search number of ∞-searchers required is NP-hard REF .
A Visibility-Based Pursuit-Evasion Problem
International Journal of Computational Geometry and Applications
Computer Science Mathematics