Motion, Unit Dual Quaternion and Motion Optimization

TL;DR

This paper introduces a novel approach to robot motion problems by representing motions as six-dimensional vectors and formulating hand-eye calibration and SLAM as unconstrained optimization problems using dual quaternions.

Contribution

It presents a new mathematical framework for motion representation and optimization, enabling classical robot problems to be solved through real unconstrained optimization.

Findings

Unified motion representation as 6D vectors.

Formulation of classical problems as unconstrained optimization.

Potential for improved solution methods in robotics.

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.