A Sampling-Based Approach to Probabilistic Pursuit Evasion

Probabilistic roadmaps (PRMs) are a sampling-based approach to motion-planning that encodes feasible paths through the environment using a graph created from a subset of valid positions. Prior research has shown that PRMs can be augmented with useful information to model interesting scenarios related to multi-agent interaction and coordination. Pursuit evasion is the problem of planning the motions of one or more agents to effectively track and/or capture an initially unseen evader in an environment. Unlike prior probabilistic approaches that assume the environment is partitioned into convex cells or square grids, we present a sampling-based technique that allows us to generalize the problem to an arbitrary partitioning of the environment. We then show how PRMs can exploit this method using Voronoi diagrams. We discuss the theoretical underpinnings of this approach and demonstrate its validity experimentally.