English

Motion, Unit Dual Quaternion and Motion Optimization

Optimization and Control 2022-12-29 v2

Abstract

We introduce motions as real six-dimensional vectors. A motion means a rotation and a translation. We define a motion operator which maps unit dual quaternions to motions, and a UDQ operator which maps motions to unit dual quaternions. By these operators, we present the formulation of motion optimization, which is actually a real unconstrained optimization formulation. Then we formulate two classical problems in robot research, i.e., the hand-eye calibration problem and the simultaneous localization and mapping (SLAM) problem as motion optimization problems. This opens a new way to solve these problems via real unconstrained optimization.

Keywords

Cite

@article{arxiv.2212.11593,
  title  = {Motion, Unit Dual Quaternion and Motion Optimization},
  author = {Liqun Qi},
  journal= {arXiv preprint arXiv:2212.11593},
  year   = {2022}
}
R2 v1 2026-06-28T07:48:29.325Z