Real-time clothoid approximation by Rational Bezier curves

Abstract

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 computational cost reduction. In addition to this, the proposed technique is tested on a real mobile robot for trajectory generation and kinematic control. To the authors' knowledge, the present approach is the first technique which allows real-time Clothoidal path computation <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">.</b>