A geometric approach to shortest bounded curvature paths
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.
 Publication:

arXiv eprints
 Pub Date:
 March 2014
 DOI:
 10.48550/arXiv.1403.4899
 arXiv:
 arXiv:1403.4899
 Bibcode:
 2014arXiv1403.4899A
 Keywords:

 Mathematics  Metric Geometry;
 Mathematics  Geometric Topology;
 49Q10
 EPrint:
 14 pages, 8 figures