Why and How to Avoid the Flipped Quaternion Multiplication
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...
| Main Authors: | , , , , , |
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| Format: | Article |
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Multidisciplinary Digital Publishing Institute (MDPI)
2018
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| Online Access: | http://hdl.handle.net/1721.1/118190 |
| _version_ | 1826198169008996352 |
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| author | Sommer, Hannes Gilitschenski, Igor Bloesch, Michael Weiss, Stephan Siegwart, Roland Nieto, Juan |
| author2 | Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory |
| author_facet | Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory Sommer, Hannes Gilitschenski, Igor Bloesch, Michael Weiss, Stephan Siegwart, Roland Nieto, Juan |
| author_sort | Sommer, Hannes |
| collection | MIT |
| description | 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 |
| first_indexed | 2024-09-23T11:00:16Z |
| format | Article |
| id | mit-1721.1/118190 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T11:00:16Z |
| publishDate | 2018 |
| publisher | Multidisciplinary Digital Publishing Institute (MDPI) |
| record_format | dspace |
| spelling | mit-1721.1/1181902022-10-01T00:30:20Z Why and How to Avoid the Flipped Quaternion Multiplication Sommer, Hannes Gilitschenski, Igor Bloesch, Michael Weiss, Stephan Siegwart, Roland Nieto, Juan Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory Gilitschenski, Igor 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 2018-09-28T14:34:14Z 2018-09-28T14:34:14Z 2018-07 2018-06 2018-09-21T07:11:44Z Article http://purl.org/eprint/type/JournalArticle 2226-4310 http://hdl.handle.net/1721.1/118190 Sommer, Hannes et al. "Why and How to Avoid the Flipped Quaternion Multiplication." Aerospace 5, 3 (July 2018): 72 © 2018 The Authors http://dx.doi.org/10.3390/aerospace5030072 Aerospace Creative Commons Attribution http://creativecommons.org/licenses/by/4.0/ application/pdf Multidisciplinary Digital Publishing Institute (MDPI) Multidisciplinary Digital Publishing Institute |
| spellingShingle | Sommer, Hannes Gilitschenski, Igor Bloesch, Michael Weiss, Stephan Siegwart, Roland Nieto, Juan Why and How to Avoid the Flipped Quaternion Multiplication |
| title | Why and How to Avoid the Flipped Quaternion Multiplication |
| title_full | Why and How to Avoid the Flipped Quaternion Multiplication |
| title_fullStr | Why and How to Avoid the Flipped Quaternion Multiplication |
| title_full_unstemmed | Why and How to Avoid the Flipped Quaternion Multiplication |
| title_short | Why and How to Avoid the Flipped Quaternion Multiplication |
| title_sort | why and how to avoid the flipped quaternion multiplication |
| url | http://hdl.handle.net/1721.1/118190 |
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