Fastest-Path Planning for Direction-Dependent Speed Functions

Irina S. Dolinskaya, Robert L. Smith

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)480-497
Number of pages18
JournalJournal of Optimization Theory and Applications
Issue number2
StatePublished - Aug 2013


  • Anisotropic medium
  • Direction-dependent
  • Obstacle-avoiding path
  • Shortest path

ASJC Scopus subject areas

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

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