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Minimal curvature-constrained networks

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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.

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Authors and Affiliations

  1. Department of Mechanical Engineering, The University of Melbourne, Melbourne, VIC, 3010, Australia

    K. G. Sirinanda, P. A. Grossman & D. A. Thomas

  2. Department of Electrical and Electronic Engineering, The University of Melbourne, Melbourne, VIC, 3010, Australia

    M. Brazil

  3. School of Mathematics and Statistics, The University of Melbourne, Melbourne, VIC, 3010, Australia

    D. Kirszenblat & J. H. Rubinstein

Authors
  1. D. Kirszenblat
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  2. K. G. Sirinanda
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  3. M. Brazil
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  4. P. A. Grossman
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  5. J. H. Rubinstein
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  6. D. A. Thomas
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Correspondence to D. Kirszenblat.

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Kirszenblat, D., Sirinanda, K.G., Brazil, M. et al. Minimal curvature-constrained networks. J Glob Optim 72, 71–87 (2018). https://doi.org/10.1007/s10898-018-0625-2

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  • DOI: https://doi.org/10.1007/s10898-018-0625-2

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