Skip to Main content Skip to Navigation
Reports

Irregularity of Optimal Trajectories in a Control Problem for a Car-like Robot

Elena Degtiariova-Kostova 1 Vladimir Kostov
1 PRISME - Geometry, Algorithms and Robotics
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : We study the problem to find (a) shortest plane curve(s) joining two given points with given tangent angles and curvatures. The tangent angle and the curvature of the path are continuous and the derivative of the curvature is bounded by $2$. At a regular (i.e. of the class $C^3$) point such a curve must be locally a piece of a clothoid or a line segment (up to isometry a clothoid is given by Fresnel's integrals $x(t)=\int _0^t\cos \tau ^2d\tau $, $y(t)=\int _0^t\sin \tau ^2d\tau $). We prove that if the distance between the initial and final points is greater than $320\sqrt{\pi }$, then a generic shortest curve contains infinitely many switching points.
Document type :
Reports
Complete list of metadata

Cited literature [1 references]  Display  Hide  Download

https://hal.inria.fr/inria-00073279
Contributor : Rapport de Recherche Inria <>
Submitted on : Wednesday, May 24, 2006 - 12:25:39 PM
Last modification on : Saturday, January 27, 2018 - 1:31:30 AM
Long-term archiving on: : Sunday, April 4, 2010 - 11:41:04 PM

Identifiers

  • HAL Id : inria-00073279, version 1

Collections

Citation

Elena Degtiariova-Kostova, Vladimir Kostov. Irregularity of Optimal Trajectories in a Control Problem for a Car-like Robot. RR-3411, INRIA. 1998. ⟨inria-00073279⟩

Share

Metrics

Record views

283

Files downloads

325