Communications in Analysis and Geometry

Volume 26 (2018)

Number 4

A Geometric approach to shortest bounded curvature paths

Pages: 679 – 697

DOI: http://dx.doi.org/10.4310/CAG.2018.v26.n4.a1

Authors

José Ayala (Instituto de Ciencias Exactas y Naturales, Universidad Arturo Prat, Iquique, Chile)

David Kirszenblat (School of Mathematics and Statistics, University of Melbourne, Parkville, Victoria, Australia)

Hyam Rubinstein (School of Mathematics and Statistics, University of Melbourne, Parkville, Victoria, Australia)

Abstract

We present a geometric proof for the classification of length minimisers in spaces of planar bounded curvature paths. Our methods can be adapted without much effort to classify length minimisers in spaces of bounded curvature paths in other surfaces. The main result in this note fills a gap by furnishing a geometric proof for a problem in geometry that hither to was missing from the literature.

Keywords

bounded curvature paths, Dubins paths, path optimisation

2010 Mathematics Subject Classification

Primary 49Q10. Secondary 51E99, 68R99, 90C47.

Full Text (PDF format)

Received 10 September 2015