Minimal curvature-constrained networks
Abstract
This paper introduces an exact algorithm for the construction of a shortest curvature-constrained network interconnecting a given set of directed points in the plane and an iterative method for doing so in 3D space. Such a network will be referred to as a minimum Dubins network, since its edges are Dubins paths (or slight variants thereof). The problem of constructing a minimum Dubins network appears in the context of underground mining optimisation, where the aim is to construct a least-cost network of tunnels navigable by trucks with a minimum turning radius. The Dubins network problem is similar to the Steiner tree problem, except that the terminals are directed and there is a curvature constraint. We propose the minimum curvature-constrained Steiner point algorithm for determining the optimal location of the Steiner point in a 3-terminal network. We show that when two terminals are fixed and the third varied, the Steiner point traces out a lima\c{c}on.
Keywords
Cite
@article{arxiv.1606.02026,
title = {Minimal curvature-constrained networks},
author = {David Kirszenblat and Kashyapa Sirinanda and Marcus Brazil and Peter Grossman and J. Hyam Rubinstein and Doreen Thomas},
journal= {arXiv preprint arXiv:1606.02026},
year = {2016}
}
Comments
20 pages, 16 figures