Smooth local-path planning for autonomous vehicles

We propose a new method for generating smooth paths for vehicle path planning. The problem of finding the 'smoothest path'' joining two given configurations is solved (a configuration is a position and a direction). Generally, we solve the problem using two ''simple'' path segments. The most important issue is how to define the smoothness cost of a path. We propose two distinct definitions: the first is the path curvature, and the second is the derivative of the path curvature. We use circular arcs with the first definition, and we use ''cubic spirals'' with the second for ''simple curves'' respectively. The set of cubic spirals has several advantages when used in smooth-path planning, one of which is curvature continuity. This theory also reveals other important concepts in robotics, such as ''symmetric configurations'' and 'symmetric means.'' This algorithm has been successfully implemented an the autonomous mobile robot Yamabico-11 at the University of California at Santa Barbara and at the Naval Postgraduate School.