IRI - On closed-form solutions to the 4D nearest rotation matrix problem

Publication

On closed-form solutions to the 4D nearest rotation matrix problem

Journal Article (2024)

Journal

Mathematical Methods in the Applied Sciences

Pages

1248-1256

Volume

Number

Doc link

https://doi.org/10.1002/mma.8524

File

Download the digital copy of the doc pdf document

Authors

Projects associated

KINODYN+: Synthesis of Optimally Agile and Graceful Robot Motions

Abstract

In this paper, we address the problem of restoring the orthogonality of a numerically noisy 4D rotation matrix by finding its nearest (in Frobenius norm) correct rotation matrix. This problem can be straightforwardly solved using the Singular Value Decomposition (SVD). Nevertheless, to avoid numerical methods, we present two new closed-form methods. One relies on the direct minimization of the mentioned Frobenius norm, and the other on the passage to double quaternion representation. A comparison of these two methods with respect to the SVD reveals that the method based on a double quaternion representation is superior in all aspects.

Author keywords

4D rotations, double quaternions, fourth-degree polynomials

Scientific reference

S. Sarabandi and F. Thomas. On closed-form solutions to the 4D nearest rotation matrix problem. Mathematical Methods in the Applied Sciences, 47(3): 1248-1256, 2024.