Obstacle distance for car-like robots

This paper shows how to compute the nonholonomic distance between a point-w ise car-like robot and polygonal obstacles, Geometric constructions to comp ute the shortest paths from a configuration (given orientation and position in the plane of the robot) to a position (i.e., a configuration with unspe cified final orientation) are first presented. The geometric structure of t he reachable set (set of points in the plane reachable by paths of given le ngth l) is then used to compute the shortest paths to straight-line segment s. Obstacle distance is defined as the length of such shortest paths. The a lgorithms are developed for robots that can move both forward and backward (Reeds&Shepp's car) or only forward (Dubins' car). They are based on the co nvexity analysis of the reachable set.