Minimal curvature-constrained networks

D. Kirszenblat (), K. G. Sirinanda, M. Brazil, P. A. Grossman, J. H. Rubinstein and D. A. Thomas
Additional contact information
D. Kirszenblat: The University of Melbourne
K. G. Sirinanda: The University of Melbourne
M. Brazil: The University of Melbourne
P. A. Grossman: The University of Melbourne
J. H. Rubinstein: The University of Melbourne
D. A. Thomas: The University of Melbourne

Journal of Global Optimization, 2018, vol. 72, issue 1, No 5, 87 pages

Abstract: 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 a gradient descent method for doing so in 3D space. Such a network will be referred to as a minimum Dubins tree, since its edges are Dubins paths (or slight variants thereof). The problem of constructing a minimum Dubins tree appears in the context of underground mining optimisation, where the objective is to construct a least-cost network of tunnels navigable by trucks with a minimum turning radius. The Dubins tree problem is similar to the Steiner tree problem, except 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 in the planar version of the problem, the Steiner point traces out a limaçon.

Keywords: Network optimisation; Optimal mine design; Dubins path; Curvature constraint; Steiner point (search for similar items in EconPapers)
Date: 2018
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10898-018-0625-2

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