Continuous-curvature path planning for car-like vehicles

We consider path planning for a car-like vehicle. Previous solutions to this problem computed paths made up of circular arcs connected by tangential line segments. Such paths have a discontinuous curvature profile. Accordingly a vehicle following such a path has to stop at each curvature discontinuity in order to re-orientate its front wheels. To remove this limitation, we add a continuous-curvature constraint to the problem at hand. In addition, we introduce a constraint on the curvature derivative, so as to reflect the fact that a car-like vehicle can only re-orientate its front wheels with a finite velocity. We propose an efficient solution to the problem at hand that relies upon the definition of a set of paths with continuous curvature and maximum curvature derivative. These paths contain at most eight pieces, each piece being either a line segment, a circular arc of maximum curvature, or a clothoid arc. They are called simple continuous curvature paths. They are used to design a local path planner. The experimental results are presented.