Interpolating Rotations with Non-abelian Kuramoto Model on the 3-Sphere

TL;DR

This paper introduces a new interpolation method for rotations using a non-Abelian Kuramoto model on the 3-sphere, providing a direct path between rotations with results comparable to spherical linear interpolation, supported by visualizations and simulations.

Contribution

The paper proposes a novel rotation interpolation algorithm based on the non-Abelian Kuramoto model on S3, offering a new approach to rotation pathfinding.

Findings

The algorithm finds the shortest, most direct rotation path.

Results are comparable to spherical linear interpolation.

Visualizations demonstrate the method's effectiveness.

Abstract

The paper presents a novel method for interpolating rotations based on the non-Abelian Kuramoto model on sphere S3. The algorithm, introduced in this paper, finds the shortest and most direct path between two rotations. We have discovered that it gives approximately the same results as a Spherical Linear Interpolation algorithm. Simulation results of our algorithm are visualized on S2 using Hopf fibration. In addition, in order to gain a better insight, we have provided one short video illustrating the rotation of an object between two positions.