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Why and How to Avoid the Flipped Quaternion Multiplication

Autonomous Systems Lab, Eidgenössische Technische Hochschule Zürich (ETHZ), 8092 Zürich, Switzerland
Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology (MIT), Cambridge, MA 02139, USA
Dyson Robotics Lab, Imperial College London, London SW7 2AZ, UK
Institute of Smart System Technologies, Alpen-Adria-Universität Klagenfurt (AAU), 9020 Klagenfurt, Austria
Author to whom correspondence should be addressed.
Aerospace 2018, 5(3), 72;
Received: 17 May 2018 / Revised: 20 June 2018 / Accepted: 28 June 2018 / Published: 5 July 2018
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. View Full-Text
Keywords: quaternion multiplication; attitude; rotation; convention quaternion multiplication; attitude; rotation; convention
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MDPI and ACS Style

Sommer, H.; Gilitschenski, I.; Bloesch, M.; Weiss, S.; Siegwart, R.; Nieto, J. Why and How to Avoid the Flipped Quaternion Multiplication. Aerospace 2018, 5, 72.

AMA Style

Sommer H, Gilitschenski I, Bloesch M, Weiss S, Siegwart R, Nieto J. Why and How to Avoid the Flipped Quaternion Multiplication. Aerospace. 2018; 5(3):72.

Chicago/Turabian Style

Sommer, Hannes, Igor Gilitschenski, Michael Bloesch, Stephan Weiss, Roland Siegwart, and Juan Nieto. 2018. "Why and How to Avoid the Flipped Quaternion Multiplication" Aerospace 5, no. 3: 72.

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