Real-time clothoid approximation by Rational Bezier curves

This paper presents a novel technique for implementing Clothoidal real-time paths for mobile robots. As first step, rational Bezier curves are obtained as approximation of the Fresnel integrals. By rescaling, rotating and translating the previously computed RBC, an on-line Clothoidal path is obtained. In this process, coefficients, weights and control points are kept invariant. This on-line approach guarantees that an RBC has the same behavior as the original Clothoid using a low curve order. The resulting Clothoidal path allows any two arbitrary poses to be joined in a plane. RBCs working as Clothoids are also used to search for the shortest bounded-curvature path with a significant comput…