On existence conditions of a class of continuous curvature paths

Local steering, which constructs a kinematically or dynamically feasible path between two configurations, is a core component of various path planning methods. This paper investigates the continuous curvature (CC) steering for car-like robots subject to constraints on velocity, curvature and derivative of the curvature. Based on the μ-tangency conditions in [9], we establish existence conditions for a class of CC paths which admit the same driving patterns as the Reeds-Shepp paths [6]. These conditions allow efficient implementation of the CC steering, which enables real-time CC path planning. The feasibility and computation efficiency of the resultant CC steering are validated by numerical simulations.