Roadmap based pursuit-evasion and collision avoidance

We study pursuit-evasion games for mobile robots and their applications to collision avoidance. In the first part of the paper, under the assumption that the pursuer and the evader (possibly subject to physical constraints) share the same roadmap to plan their strategies, we present sound and complete strategies for three different games. In the second part, we utilize the pursuit-evasion results to post-process the workspace and/or configuration space and obtain a collision probability map of the environment. Next, we present a probabilistic method to utilize this map and plan trajectories which minimize the collision probability for independent robots.