Path Generation Using Linear Curvature and Torsion Segments

In two-dimensional(2D) space, the clothoid is a preferred trajectory curve because its curvature varies linearly with its curve length. However, in three-dimensional(3D) space, both curvature and torsion must be considered. This paper deals with path generation using linear curvature and torsion segments which can be considered a 3D extension of the 2D clothoid. In our study, the path segments are generated by solving the Frenet-Serret equation. In every path segment, its curvature and torsion varies linearly with its curve length. In order to obtain more free parameters, plural curve segments are connected in series to make a compound curve. The curve is used to connect two given points which may have given Frenet-Frame, curvature and torsion constraints. These curves are also used to construct a smooth transition passing through an arbitrary point sequence. The resultant path possesses C2 as well as torsion continuity and matches all given Frenet-frame, curvature and torsion constraints at the given points.