An introduction to using dual quaternions to study kinematics

TL;DR

The paper develops a practical framework for kinematics using dual quaternions to represent poses, twists, and wrenches within the Lie group SE(3). It demonstrates that unit dual quaternions yield a bilinear pose composition, efficient normalization, and a natural bridge to twists via the relation d/dt eta = eta phi. The work provides methods for pose interpolation, perturbation analysis, and slerp of dual quaternions, supported by proofs of core algebraic properties and a projection technique from matrices to rotations. These contributions offer a compact, computationally efficient toolkit for forward kinematics, trajectory generation, and control in robotics and computer graphics.

Abstract

We explain the use of dual quaternions to represent poses, twists, and wrenches.

Theorems & Definitions (2)

• proof : Proof of Equations \ref{['norm mult']} and \ref{['normalize mult']}
• proof : Proof of Equation \ref{['twist as dual quaternion']}