Set of reachable positions for a car

This paper shows how to compute the reachable positions for a model of a car with a lower bounded turning radius that moves forward and backward with a constant velocity. First, the authors compute the shortest paths when the starting configuration (i.e., position and direction) is completely specified and the goal is only defined by the position with the direction being arbitrary. Then the authors compute the boundary of the region reachable by such paths. Such results are useful in motion planning for nonholonomic mobile robots