A geometric approach to shortest bounded curvature paths

José Ayala; David Kirszenblat; J. Hyam Rubinstein

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arXiv · 1403.4899

A geometric approach to shortest bounded curvature paths

José Ayala·David Kirszenblat·J. Hyam Rubinstein

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Abstract

Consider two elements in the tangent bundle of the Euclidean plane $(x,X),(y,Y)\in T{\mathbb R}^2$. In this work we address the problem of characterizing the paths of bounded curvature and minimal length starting at $x$, finishing at $y$ and having tangents at these points $X$ and $Y$ respectively. This problem was first investigated in the late 50's by Lester Dubins. In this note we present a constructive proof of Dubins' result giving special emphasis on the geometric nature of this problem.

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José Ayala, David Kirszenblat, J. Hyam Rubinstein. 2015-08-27. A geometric approach to shortest bounded curvature paths. https://arxiv.org/abs/1403.4899

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