Why and How to Avoid the Flipped Quaternion Multiplication
Name
aerospace-05-00072.pdf
Size
400.3 KB
Format
Adobe PDF
Checksum (MD5)
a21d47a75acc00cad40c983ca97fafd7
Author(s)
Sommer, Hannes
Gilitschenski, Igor
Bloesch, Michael
Weiss, Stephan
Siegwart, Roland
Nieto, Juan
Date Issued
July 2018
Journal
Aerospace
Publisher
Multidisciplinary Digital Publishing Institute (MDPI)
Citation
Sommer, Hannes et al. "Why and How to Avoid the Flipped Quaternion Multiplication." Aerospace 5, 3 (July 2018): 72 © 2018 The Authors
Version
Final published version
Abstract
Over the last decades quaternions have become a crucial and very successful tool for attitude representation in robotics and aerospace. However, there is a major problem that is continuously causing trouble in practice when it comes to exchanging formulas or implementations: there are two quaternion multiplications commonly in use, Hamilton’s multiplication and its flipped version, which is often associated with NASA’s Jet Propulsion Laboratory. This paper explains the underlying problem for the popular passive world-to-body usage of rotation quaternions, and promotes an alternative solution compatible with Hamilton’s multiplication. Furthermore, it argues for discontinuing the flipped multiplication. Additionally, it provides recipes for efficiently detecting relevant conventions and migrating formulas or algorithms between them. Keywords: quaternion multiplication; attitude; rotation; convention
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Terms of Use
Creative Commons Attribution
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.3390/aerospace5030072
