Presents a variant of probabilistic roadmap algorithms that appeared as a promising approach to motion planning. We exploit a free-space structuring of the configuration space into visibility domains in order to produce small roadmaps. The algorithm has been implemented within a software platform allowing us to address a large class of mechanical systems. Experiments show the efficiency of the approach in capturing narrow passages of collision-free configuration spaces.

This paper shows how to compute the nonholonomic distance between a pointwise car-like robot and polygonal obstacles. Geometric constructions to compute the shortest paths from a configuration (given orientation and position in the plane of the robot) to a position (i.e., a configuration with unspecified final orientation) are first presented. The geometric structure of the reachable set (set of points in the plane reachable by paths of given length /spl Lscr/) is then used to compute the shortest paths to straight-line segments. Obstacle distance is defined as the length of such shortest paths. The algorithms are developed for robots that can move both forward and backward (Reeds and Shepp's car) or only forward (Dubins' car). They are based on the convexity analysis of the reachable set.

This paper deals with distance computation between a forward moving car-like robot and polygonal obstacles. We propose efficient geometric algorithms to compute the shortest paths to obstacles. We then derive the "visibility" domain in the presence of obstacles, i.e. the set of positions reachable from a starting configuration, by a collision-free shortest path unaffected by the presence of the obstacles.