From Reeds and Shepp's to continuous-curvature paths

This paper presents Continuous Curvature (CC) Steer, a steering method for car-like vehicles, i.e., an algorithm planning paths in the absence of obstacles. CC Steer is the first to compute paths with: 1) continuous curvature; 2) upper-bounded curvature; and 3) upper-bounded curvature derivative. CC Steer also verifies a topological property that ensures that when it is used within a general motion-planning scheme, it yields a complete collision-free path planner. The coupling of CC Steer with a general planning scheme yields a path planner that computes collision-free paths verifying the properties mentioned above. Accordingly, a car-like vehicle can follow such paths without ever having to stop in order to reorient its front wheels. Besides, such paths can be followed with a nominal speed which is proportional to the curvature derivative limit. The paths computed by CC Steer are made up of line segments, circular arcs, and clothoid arcs. They are not optimal in length. However, it is shown that they converge toward the optimal "Reeds and Shepp" paths when the curvature derivative upper bound tends to infinity. The capabilities of CC Steer to serve as an efficient steering method within two general planning schemes are also demonstrated.

I. Introduction

Ever since Laumond's pioneering paper in 1986 [1], much research has addressed collision-free path planning for nonholonomic systems in general, and car-like vehicles in particular. Nonholonomic systems are subject to kinematic constraints that restrict their admissible directions of motion. Nonholonomy makes path planning more difficult, since the paths planned must take into account the constraints imposed both by the obstacles and the nonholonomic constraints (the reader is referred to [2] for a recent and extensive review on this topic). Car-like vehicles are archetypal nonholonomic systems. They can only move forward or backward in a direction perpendicular to the orientation of their rear wheels' axle; besides, their turning radius is lower bounded because of the mechanical limits on the steering angle.