Optimal robust path planning in general environments

We address robust path planning for a mobile agent in a general environment by finding minimum cost source-destination paths having prescribed widths. The main result is a new approach that optimally solves the robust path planning problem using an efficient network flow formulation. Our algorithm represents a significant departure from conventional shortest-path or graph search based methods; it not only handles environments with solid polygonal obstacles, but also generalizes to arbitrary cost maps that may arise in modeling incomplete or uncertain knowledge of the environment. Simple extensions allow us to address higher dimensional problem instances and minimum-surface computations; the latter is a result of independent interest. We use an efficient implementation to exhibit optimal path-planning solutions for a variety of test problems. The paper concludes with open issues and directions for future work.