2A1-B01 Robot Trajectory Generation with Smoothly Changing Curvature Using the Clothoid Curve(New Control Theory and Motion Control)

Abstract

In this paper we propose optimization methods for trajectory design using clothoid curves in two-dimensional space. As a trajectory path, the clothoid curve is superior to other ones because its curvature varies linearly with its curve length. However, a single clothoid segment cannot generally satisfyes both tangent and curvature conditions at its end points because the number of its parameters is insufficient. In order to solve this type of the problem, "triple clothoid" was introduced to match both tangent and curvature boundary condistions. The triple clothoid is a set of three clothoid segments connected internally with curvature as well as tangent continuity. It has sufficient parameters needed for tangent and curvature matching at its end point. The triple clothoid segments were used to construct a smooth transition passing through arbitrary point sequence. The result trajectory possesses curvature continuity and matches all tangent and curvature designations at the giving points. However, the triple clothoid curve that passes through specified points is not uniquely determined. Therefore we propose optimization methods to minimize the trajectory path length and the energy consumption measure introduced in this paper.