Interpolating clothoid splines with curvature continuity

An efficient algorithm for the computation of a C-2 interpolating clothoid spline is herein presented. The spline is obtained following an optimisation process, subject to continuity constraints. Among the 9 various targets/problems considered, there are boundary conditions, minimum length path, minimum jerk, and minimum curvature (energy). Some of these problems are solved with just a couple of Newton iterations, whereas the more complex minimisations are solved with few iterations of a nonlinear solver. The solvers are warmly started with a suitable initial guess, which is extensively discussed, making the algorithm fast. Applications of the algorithm are shown relating to fonts, path planning for human walkers, and as a tool for the time-optimal lap on a Formula 1 circuit track.