Nonholonomic path planning among obstacles subject to curvature restrictions

This paper addresses the problem of finding a nonholonomic path subject to a curvature restriction, to be tracked by a wheeled autonomous navigation vehicle. This robot is able to navigate in a structured environment, with obstacles modeled as polygons, thus constituting a model based system. The path planning methodology begins with the conditioning of the polygonal environment by offsetting each polygon in order to avoid the possibility of collision with the mobile. Next, the modified polygonal environment is used to compute a preliminary shortest path (PA) between the two extreme positions of the trajectory in the plane (x, y). This preliminary path (PA) does not yet consider the restrictions on the curvature and is formed only by straight line segments. A smoothing process follows in order to obtain a path (PS) that satisfies curvature restrictions which consist basically of joining the straight line segments by circular arcs of minimum radius R (filleting). Finally, the initial and final orientation of the vehicle are accounted for. This is done using a technique we have called the Star Algorithm, because of the geometric shape of the resulting maneuvers. A final complete path (PC) is thus obtained.