The classification of homotopy classes of bounded curvature paths

José Ayala; J. Hyam Rubinstein

The classification of homotopy classes of bounded curvature paths

Metric Geometry 2017-08-23 v3

Authors: José Ayala , J. Hyam Rubinstein

Abstract

A bounded curvature path is a continuously differentiable piecewise $C^2$ path with bounded absolute curvature that connects two points in the tangent bundle of a surface. In this note we give necessary and sufficient conditions for two bounded curvature paths, defined in the Euclidean plane, to be in the same connected component while keeping the curvature bounded at every stage of the deformation. Following our previous results here we finish a program started by Lester Dubins in 1961.

Keywords

bounded curvature paths homotopy classes connected components Euclidean plane curvature constraints Dubins paths

Cite

@article{arxiv.1403.5314,
  title  = {The classification of homotopy classes of bounded curvature paths},
  author = {José Ayala and J. Hyam Rubinstein},
  journal= {arXiv preprint arXiv:1403.5314},
  year   = {2017}
}

Comments

To appear in the Israel Journal of Mathematics. arXiv admin note: substantial text overlap with arXiv:1403.4930, arXiv:1403.4911

The classification of homotopy classes of bounded curvature paths

Abstract

Keywords

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