Smooth local path planning for autonomous vehicles

Two cost functions of paths for smoothness are defined: path curvature and the derivative of path curvature. Through these definitions, two classes of simple paths are obtained, namely the set of circular arcs and the set of cubic spirals. A cubic spiral is a curve whose tangent direction is described by a cubic function of path distance s. These sets of simple paths are used for solving path planning problems of symmetric posture (position and orientation) pairs. For a nonsymmetric posture pair, two simple paths are used as a solution, based on the fact that the locus of split postures is a circle or a straight line. A posture q is said to be a split posture of a pair (p₁,p₂) of postures, if p₁ and q are symmetric and so are q and p₂. The resultant solutions are smoother than those obtained using clothoid curves. This algorithm has been successfully implemented on the autonomous mobile robot Yamabico-11