Projecting onto the unit dual quaternion set

Ziyang Li; Chunfeng Cui; Jiaxin Xie

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arXiv · 2510.20425

Projecting onto the unit dual quaternion set

Ziyang Li·Chunfeng Cui·Jiaxin Xie

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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 the unit dual quaternion set. In this paper, we systematically study such projections under the $2^R$-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.

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Ziyang Li, Chunfeng Cui, Jiaxin Xie. 2025-10-23. Projecting onto the unit dual quaternion set. https://arxiv.org/abs/2510.20425

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