Relaxing nonholonomic constraints: Towards continuous-curvature Dubins paths

In this paper we propose a new method to tackle the problem of discontinuous curvature observed in the time-optimal Dubins trajectories of car-like robots. The discontinuous curvature profile renders the paths untraceable by a real robot due to the existence of infinite accelerations at the transition points. To make way for a continuous curvature profile, we relax the idealized nonholonomic constraint of no-skidding, thereby giving rise to a more realistic model of the robot. Followed by that, by applying the tools of Pontryagin´s Minimum Principle and assuming control over the curvature of the contact point, we find that in addition to the conventional time-optimal motion primitives of straight lines and arcs of minimum turning radius, a new family of motion primitives arises, with the unique feature of allowing for continuous-curvature transition points.