Publication
A spectral decomposition approach to the accurate conversion of 4D rotation matrices to double quaternions
Conference Article
Conference
Conference on Applied Geometric Algebras in Computer Science and Engineering (AGACSE)
Edition
8th
Doc link
http://agacse2021.fme.vutbr.cz/main.php
File
Authors
Projects associated
Abstract
The problem of approximating dual quaternions by double quaternions emerges when trying to approximate 3D displacements by 4D rotations to simplify some problems arising in Robotics and Computer Graphics. This has triggered a renewed interest in 4D rotations. While 3D rotations can be represented using ordinary quaternions, 4D rotations require the use of double quaternions. Analogously to the 3D case, the mapping from double quaternions to rotation matrices cannot be smoothly inverted because it is a 2-to-1 mapping. This induces numerical problems near singularities that are exacerbated when the elements of the rotation matrices are noisy. This paper focuses on the inversion of the mentioned mapping, including the important case in which the rotation matrices are contaminated by noise, and presents a new spectral decomposition approach which compares favorably with Rosen-Elfrinkhof method both in terms of time and accuracy.
Categories
robot kinematics.
Author keywords
Quaternions, Rotation matrices
Scientific reference
S. Sarabandi and F. Thomas. A spectral decomposition approach to the accurate conversion of 4D rotation matrices to double quaternions, 8th Conference on Applied Geometric Algebras in Computer Science and Engineering, 2021, Brno, Czech Republic.
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