三連クロソイドによる自由点列補間

概要

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This paper describes trajectory design using clothoid segments. As a trajectory path, clothoid is superior to the other curves because its curvature varies linearly with its curve length. However, a single clothoid segment is not able to match both tangent and curvature designation at its terminals because it has no sufficient parameters. In our study, “triple clothoid” is introduced to match both tangent and curvature designations. The triple clothoid is a set of three clothoid segments connected internally with curvature continuity. It has sufficient parameters needed for tangent and curvature matching at its terminals. The triple clothoid segments are used to construct a smooth transition passing through arbitrary point sequence. The resultant trajectory possesses curvature continuity and matches all tangent and curvature designations at the giving points. Those results are extended from two-dimensional (2D) to three-dimensional (3D) space. In 3D space, a predefined 3D clothoid is used to construct triple 3D clothoid. The resultant 3D trajectory also possesses kinematical superiority because of its differential linearity in both pitch and yaw angles. The triple clothoid can also be used for connecting two straight segments with curvature continuity.
公益社団法人精密工学会の論文