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Optimal Geodesic Curvature Constrained Dubins’ Paths on a Sphere

Author

Listed:
  • Swaroop Darbha

    (Texas A & M University)

  • Athindra Pavan

    (Texas A & M University)

  • Rajagopal Kumbakonam

    (Texas A & M University)

  • Sivakumar Rathinam

    (Texas A & M University)

  • David W. Casbeer

    (Air Force Research Laboratories)

  • Satyanarayana G. Manyam

    (Infoscitex Corp.)

Abstract

In this article, we consider the motion planning of a rigid object on the unit sphere with a unit speed. The motion of the object is constrained by the maximum absolute value, $$U_{max}$$ U max , of geodesic curvature of its path; this constrains the object to change the heading at the fastest rate only when traveling on a tight smaller circular arc of radius $$r \frac{1}{2}$$ r > 1 2 , while paths of the above type may cease to exist depending on the boundary conditions and the value of r, optimal paths may be concatenations of more than three circular arcs.

Suggested Citation

  • Swaroop Darbha & Athindra Pavan & Rajagopal Kumbakonam & Sivakumar Rathinam & David W. Casbeer & Satyanarayana G. Manyam, 2023. "Optimal Geodesic Curvature Constrained Dubins’ Paths on a Sphere," Journal of Optimization Theory and Applications, Springer, vol. 197(3), pages 966-992, June.
    • Handle: RePEc:spr:joptap:v:197:y:2023:i:3:d:10.1007_s10957-023-02206-3
    DOI: 10.1007/s10957-023-02206-3
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