Incremental Sampling-Based Algorithms for a Class of Pursuit-Evasion Games

Pursuit-evasion games have been used for modeling various forms of conflict arising between two agents modeled as dynamical systems. Although analytical solutions of some simple pursuit-evasion games are known, most interesting instances can only be solved using numerical methods requiring significant offline computation. In this paper, a novel incremental sampling-based algorithm is presented to compute optimal open-loop solutions for the evader, assuming worst-case behavior for the pursuer. It is shown that the algorithm has probabilistic completeness and soundness guarantees. As opposed to many other numerical methods tailored to solve pursuit-evasion games, incremental sampling-based algorithms offer anytime properties, which allow their real-time implementations in online settings.