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Fastest-Path Planning for Direction-Dependent Speed Functions

Author

Listed:
  • Irina S. Dolinskaya

    (Northwestern University)

  • Robert L. Smith

    (University of Michigan)

Abstract

We discuss path planning in a direction-dependent environment illustrated by the fastest-path problem with anisotropic speed function. The difficulty of optimal-path finding in a direction-dependent medium comes from the fact that our travel-time function is asymmetric and, in general, violates the triangle inequality. We present an analytical form solution for the fastest-path finding problem in an obstacle-free domain without making any assumptions on the structure of the speed function. Subsequently, we merge these results with visibility graph search methods to develop an obstacle-avoiding fastest-path finding algorithm for an anisotropic speed function. Optimal routing of a vessel in a stationary random seaway is discussed throughout the paper to motivate and demonstrate applications of our work.

Suggested Citation

  • Irina S. Dolinskaya & Robert L. Smith, 2013. "Fastest-Path Planning for Direction-Dependent Speed Functions," Journal of Optimization Theory and Applications, Springer, vol. 158(2), pages 480-497, August.
    • Handle: RePEc:spr:joptap:v:158:y:2013:i:2:d:10.1007_s10957-012-0248-6
    DOI: 10.1007/s10957-012-0248-6
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    References listed on IDEAS

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    1. Philpott, A. B. & Sullivan, R. M. & Jackson, P. S., 1993. "Yacht velocity prediction using mathematical programming," European Journal of Operational Research, Elsevier, vol. 67(1), pages 13-24, May.
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