IRI - Solution methods to the nearest rotation matrix problem in R3: A comparative survey

Publication

Solution methods to the nearest rotation matrix problem in R3: A comparative survey

Journal Article (2023)

Journal

Numerical Linear Algebra with Applications

Pages

e2492

Volume

Number

Doc link

http://dx.doi.org/10.1002/nla.2492

File

Download the digital copy of the doc pdf document

Authors

Projects associated

KINODYN+: Synthesis of Optimally Agile and Graceful Robot Motions

Abstract

Nowadays, the Singular Value Decomposition (SVD) is the standard method of choice for solving the nearest rotation matrix problem. Nevertheless, many other methods are available in the literature for the 3D case. This paper reviews the most representative ones, proposes alternative ones, and presents a comparative analysis to elucidate their relative computational costs and error performances. This analysis leads to the conclusion that some algebraic closed-form methods are as robust as the SVD, but significantly faster and more accurate.

Author keywords

Rotation matrices, quaternions, singular value decomposition

Scientific reference

S. Sarabandi and F. Thomas. Solution methods to the nearest rotation matrix problem in R3: A comparative survey. Numerical Linear Algebra with Applications, 30(5): e2492, 2023.