Why and How to Avoid the Flipped Quaternion Multiplication
This addresses a practical issue for researchers and engineers in robotics and aerospace by eliminating confusion in exchanging formulas and implementations, though it is incremental as it builds on existing conventions.
The paper tackles the problem of two conflicting quaternion multiplication conventions (Hamilton's original and the flipped version) causing confusion in robotics and aerospace, and proposes discontinuing the flipped multiplication while providing methods for detection and migration between conventions.
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 in common use, Hamilton's original multiplication and its flipped version, which is often associated with NASA's Jet Propulsion Laboratory. We believe that this particular issue is completely avoidable and only exists today due to a lack of understanding. This paper explains the underlying problem for the popular passive world to body usage of rotation quaternions, and derives an alternative solution compatible with Hamilton's multiplication. Furthermore, it argues for entirely discontinuing the flipped multiplication. Additionally, it provides recipes for efficiently detecting relevant conventions and migrating formulas or algorithms between them.