Optimal trajectory planning with quintic G2-splines

This paper deals with the generation of optimal paths for the automated steering of autonomous vehicles. The path is parametrized by quintic G²-splines, or η-spline, devised to guarantee the overall second order geometric continuity of a composite path interpolating an arbitrary sequence of points. Starting from the closed-form η-parametrization of the spline an optimization criterion is proposed to design smooth curves. The aim is to plan curves where the curvature variability is kept as small as possible. With good approximation, in a flatness based control scheme, this corresponds to minimize the change-rate of the steering control. Various examples are included to highlight the ductility and effectiveness of the planning