On Motion Planning for Dexrerous Manipulation, Part I: 3 Simulation Results

We address robust path planning for a mobile agent in a general environment by nding minimum cost source-destination paths having prescribed widths. The main result is a new approach which optimally solves the robust path planning problem using an e cient network ow formulation. Our algorithm represents a signi cant 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 which 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 e cient implementation to exhibit optimal path-planning solutions for a variety of test problems. The paper concludes with open issues and directions for future work.