On certain hyperelliptic signals that are natural controls for nonholonomic motion planning View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2015-09

AUTHORS

Jean-Paul Gauthier, Felipe Monroy-Pérez

ABSTRACT

In this paper, we address the general problem of approximating, in a certain optimal way, non-admissible motions of a kinematic system with nonholonomic constraints. Since this kind of problems falls into the general subriemannian geometric setting, it is natural to consider optimality in the sense of approximating by means of subriemannian geodesics. We consider systems modeled by a subriemannian Goursat structure, a particular case being the well-known system of a car with trailers, along with the associated parallel parking problem. Several authors approximate the successive Lie brackets using trigonometric functions. By contrast, we show that more natural optimal motions are related with closed hyperelliptic plane curves with a certain number of loops. More... »

PAGES

415-437

References to SciGraph publications

  • 1994-02. The tangent space in sub-riemannian geometry in JOURNAL OF MATHEMATICAL SCIENCES
  • 2005-01. On the Codimension One Motion Planning Problem in JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS
  • 1993. Lie Bracket Extensions and Averaging: The Single-Bracket Case in NONHOLONOMIC MOTION PLANNING
  • 1998. Guidelines in nonholonomic motion planning for mobile robots in ROBOT MOTION PLANNING AND CONTROL
  • 2004. Control Theory from the Geometric Viewpoint in NONE
  • 2003-12. Measures of transverse paths in sub-Riemannian geometry in JOURNAL D'ANALYSE MATHÉMATIQUE
  • 2006-07. On the Motion Planning Problem, Complexity, Entropy, and Nonholonomic Interpolation in JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS
  • 2005-04. On the One-Step-Bracket-Generating Motion Planning Problem in JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00498-015-0145-2

    DOI

    http://dx.doi.org/10.1007/s00498-015-0145-2

    DIMENSIONS

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