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.
Highlights
Introduction“The quaternion [1] is one of the most important representations of the attitude in spacecraft attitude estimation and control.” With these words Malcolm D
Duality of Rotation RepresentationsPhysical rotations are conceptually rather unambiguous
The alternative solution for the original problem represented by Equation (1) we suggest is the use of a different correspondence rule, C H ∶ U ∋ q ↦ CS (q)
Summary
“The quaternion [1] is one of the most important representations of the attitude in spacecraft attitude estimation and control.” With these words Malcolm D. “The quaternion [1] is one of the most important representations of the attitude in spacecraft attitude estimation and control.”. Shuster opened his introduction of [2], ‘The nature of the quaternion’ (in 2008). It details on a conventional shift from Hamilton’s original quaternion multiplication, ⊙ In this paper, we advocate to undo this split and return to only using Hamilton’s original multiplication.
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