English

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 2R2^R-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.

Keywords

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}
}
R2 v1 2026-07-01T07:01:53.181Z