Publication

Approaching dual quaternions from matrix algebra

Journal Article (2014)

Journal

IEEE Transactions on Robotics

Pages

1037-1048

Volume

30

Number

5

Doc link

http://dx.doi.org/10.1109/TRO.2014.2341312

File

Download the digital copy of the doc pdf document

Abstract

Dual quaternions give a neat and succinct way to encapsulate both translations and rotations into a unified representation that can easily be concatenated and interpolated. Unfortunately, the combination of quaternions and dual numbers seem quite abstract and somewhat arbitrary when approached for the first time. Actually, the use of quaternions or dual numbers separately are already seen as a break in mainstream robot kinematics, which is based on homogeneous transformations. This paper shows how dual quaternions arise in a natural way when approximating 3D homogeneous transformations by 4D rotation matrices. This results in a seamless presentation of rigid-body transformations based on matrices and dual quaternions which permits building intuition about the use of quaternions and their generalizations.

Categories

automation.

Author keywords

spatial kinematics, quaternions, biquaternions, double quaternions, dual quaternions, Cayley factorization.

Scientific reference

F. Thomas. Approaching dual quaternions from matrix algebra. IEEE Transactions on Robotics, 30(5): 1037-1048, 2014.