The classification of homotopy classes of bounded curvature paths


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 work in [3], [2] and [4] this work finishes a program started by Lester Dubins in [6] in 1961.

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Correspondence to Hyam Rubinstein.

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Ayala, J., Rubinstein, H. The classification of homotopy classes of bounded curvature paths. Isr. J. Math. 213, 79–107 (2016).

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  • Unit Circle
  • Minimal Length
  • Homotopy Class
  • Curvature Path
  • Proximity Condition