Solutions for path planning using spline parameterization

This chapter presents a B-spline path synthesis approach for nonholonomic car-like vehicles. Recent findings in robotic research suggest that C2 continuity is a realistic representation of robotic paths. A novel solution that guarantees C2 parametric continuity for a cubic path, whilst satisfying kinodynamic constraints imposed on the vehicle, is proposed here. This chapter investigates path synthesis for front wheel steered vehicles. It is required to generate paths with continuous, bounded curvatures. Our approach is based on clamped B-spline curves. We leverage the curves' properties to resolve the considered problem. In order to ensure continuity, a single curve segment is utilized for the entire path. Path curvature is formulated with respect to the B-spline curve parameters. This approach mimics human operating and minimizes disturbances on passengers. We present here a method of curvature estimation that is more accurate and time efficient than previously published solutions. Two analytical bounding solutions are proposed. Both methods are shown to minimize path length and deviation, whilst maintaining curvature and parametric continuity.