Finding narrow passages with Probabilistic Roadmaps: The small-step retraction method

Probabilistic Roadmaps (PRM) have been successfully used to plan complex robot motions in configuration spaces of small and large dimensionalities. However, their efficiency decreases dramatically in spaces with narrow passages. This paper presents a new method-small-step retraction-that helps PRM planners find paths through such passages. This method consists of slightly "fattening" robot's free space, constructing a roadmap in fattened free space, and finally repairing portions of this roadmap by retracting them out of collision into actual free space. Fattened free space is not explicitly computed. Instead, the geometric models of workspace objects (robot links and/or obstacles) are "thinned" around their medial axis. A robot configuration lies in fattened free space if the thinned objects do not collide at this configuration. Two repair strategies are proposed. The "optimist" strategy waits until a complete path has been found in fattened free space before repairing it. Instead, the "pessimist" strategy repairs the roadmap as it is being built. The former is usually very fast, but may fail in some pathological cases. The latter is more reliable, but not as fast. A simple combination of the two strategies yields an integrated planner that is both fast and reliable. This planner was implemented as an extension of a pre-existing single-query PRM planner. Comparative tests show that it is significantly faster (sometimes by several orders of magnitude) than the pre-existing planner.