Journal article

Minimal curvature-constrained networks

D Kirszenblat, KG Sirinanda, M Brazil, PA Grossman, JH Rubinstein, DA Thomas

JOURNAL OF GLOBAL OPTIMIZATION | SPRINGER | Published : 2018

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 con..

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