Projecting onto the Unit Dual Quaternion Set
Numerical Analysis
2025-10-24 v1 Numerical Analysis
Abstract
Dual quaternions have gained significant attention due to their wide applications in areas such as multi-agent formation control, 3D motion modeling, and robotics. A fundamental aspect in dual quaternion research involves the projection onto unit dual quaternion sets. In this paper, we systematically study such projections under the -norm, which is commonly used in practical applications. We identify several distinct cases based on the relationship between the standard and dual parts in vector form, and demonstrate the effectiveness of the proposed algorithm through numerical experiments.
Cite
@article{arxiv.2510.20425,
title = {Projecting onto the Unit Dual Quaternion Set},
author = {Ziyang Li and Chunfeng Cui and Jiaxin Xie},
journal= {arXiv preprint arXiv:2510.20425},
year = {2025}
}