Projecting onto the Unit Dual Quaternion Set
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918167271440384 |
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| author | Li, Ziyang Cui, Chunfeng Xie, Jiaxin |
| author_facet | Li, Ziyang Cui, Chunfeng Xie, Jiaxin |
| contents | 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 $2^R$-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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_20425 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Projecting onto the Unit Dual Quaternion Set Li, Ziyang Cui, Chunfeng Xie, Jiaxin Numerical Analysis 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 $2^R$-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. |
| title | Projecting onto the Unit Dual Quaternion Set |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2510.20425 |