Optimal Geodesic Curvature Constrained Dubins’ Paths on a Sphere

Swaroop Darbha (), Athindra Pavan (), Rajagopal Kumbakonam (), Sivakumar Rathinam (), David W. Casbeer () and Satyanarayana G. Manyam ()
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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.

Journal of Optimization Theory and Applications, 2023, vol. 197, issue 3, No 5, 966-992

Abstract: 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.

Keywords: Dubins paths; Geodesic curvature constraints; Path planning on sphere (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10957-023-02206-3

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