Pursuit-Evasion with Fixed Beams

We introduce a complete algorithm for solving a pursuit-evasion problem in a simply connected two-dimensional environment, for the case of a single pursuer equipped with fixed beam sensors. The input for our algorithm is an environment and a collection of sensor directions, in which each is capable of line-of-sight detection in a fixed direction. The output is a pursuer motion strategy that ensures the detection of an evader that moves with unbounded speed, or a statement that no such strategy exists. The intuition of the algorithm is to decompose the environment into a collection of convex conservative regions, within which the evader cannot sneak between any pair of adjacent sensors. This decomposition induces a graph we call the pursuit-evasion graph (PEG), such that any correct solution strategy can be expressed as a path through the PEG. For an instance defined by m beams and an environment with n vertices, the algorithm runs in time O(2(m)n(2)). We implemented the algorithm in simulation and present some computed examples illustrating the algorithm's correctness.