An efficient algorithm for the computation of a C2 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.
Interpolating clothoid splines with curvature continuity / Bertolazzi, Enrico; Frego, Marco. - In: MATHEMATICAL METHODS IN THE APPLIED SCIENCES. - ISSN 0170-4214. - STAMPA. - 41:4(2018), pp. 1723-1737. [10.1002/mma.4700]
Interpolating clothoid splines with curvature continuity
Bertolazzi, Enrico;Frego, Marco
2018-01-01
Abstract
An efficient algorithm for the computation of a C2 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione