Trajectory Generation based on Rational Bezier Curves as Clothoids

Abstract

This paper explains a fast overtaking algorithm for IVHS based on clothoidal trajectories. In spite of the fact that clothoidal trajectory generation requires complicated computation of Fresnel integrals, in this paper, an on-line clothoidal path is obtained just by scaling a general parametric curve. This is based on a general offline approximation of the Fresnel integrals into rational Bezier curves (RBC) which are later used in the generation of on-line clothoidal paths. In addition, in order to obtain a fast algorithm, a new methodology to approximate the Fresnel integrals into RBC is proposed. This approach guarantees that the resulting curve has the same behavior than the clothoid. In particular for overtaking maneuvers, a clothoidal path composed of two equal elementary paths is generated. Each one constructed joining two piecewise identical clothoids. A 3D simulation environment has been used for testing the trajectory generation algorithm described in the paper. As can be seen, the obstacle avoidance module generates free-collision intermediate positions which are reached by clothoidal paths.