Relaxing nonholonomic constraints: Towards continuous-curvature Dubins paths
Salah Bazzi, Elie Shammas, Daniel Asmar · 2015
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.