Equivalence of Dubins Path on Sphere with Geographic Coordinates and Moving Frames

TL;DR

This paper demonstrates that two different methods for planning paths of a Dubins vehicle on a sphere—using spherical coordinates and moving frames—are mathematically equivalent, enabling results to be transferred between approaches.

Contribution

It establishes the equivalence between spherical coordinate and moving frame methods for Dubins path planning on a sphere, facilitating broader application of existing results.

Findings

Proves the mathematical equivalence of the two methods

Enables transfer of results between coordinate systems

Simplifies path planning analysis for spherical Dubins vehicles

Abstract

In this article, two methods of addressing path planning for a Dubins vehicle moving on a sphere are considered, wherein either spherical coordinates or a moving frame are considered to describe the vehicle's motion. The primary contribution of this article is to show the equivalence of these two approaches, which in turn shows that the results known for the moving frame-based description transfer to the model utilizing spherical coordinates.