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Minimal curvature-constrained networks

Author

Listed:
  • 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)

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.

Suggested Citation

  • D. Kirszenblat & K. G. Sirinanda & M. Brazil & P. A. Grossman & J. H. Rubinstein & D. A. Thomas, 2018. "Minimal curvature-constrained networks," Journal of Global Optimization, Springer, vol. 72(1), pages 71-87, September.
    • Handle: RePEc:spr:jglopt:v:72:y:2018:i:1:d:10.1007_s10898-018-0625-2
    DOI: 10.1007/s10898-018-0625-2
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