Unit Dual Quaternion Directed Graphs, Formation Control and General Weighted Directed Graphs
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913572258316288 |
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| author | Qi, Liqun Cui, Chunfeng Ouyang, Chen |
| author_facet | Qi, Liqun Cui, Chunfeng Ouyang, Chen |
| contents | We study the multi-agent formation control problem in a directed graph. The relative configurations are expressed by unit dual quaternions (UDQs). We call such a weighted directed graph a unit dual quaternion directed graph (UDQDG). We show that a desired relative configuration scheme is reasonable or balanced in a UDQDG if and only if the dual quaternion Laplacian is similar to the unweighted Laplacian of the underlying directed graph. A direct method and a unit gain graph method are proposed to solve the balance problem of general unit weighted directed graphs. We then study the balance problem of general non-unit weighted directed graphs. Numerical experiments for UDQDG are reported. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_05132 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unit Dual Quaternion Directed Graphs, Formation Control and General Weighted Directed Graphs Qi, Liqun Cui, Chunfeng Ouyang, Chen Rings and Algebras We study the multi-agent formation control problem in a directed graph. The relative configurations are expressed by unit dual quaternions (UDQs). We call such a weighted directed graph a unit dual quaternion directed graph (UDQDG). We show that a desired relative configuration scheme is reasonable or balanced in a UDQDG if and only if the dual quaternion Laplacian is similar to the unweighted Laplacian of the underlying directed graph. A direct method and a unit gain graph method are proposed to solve the balance problem of general unit weighted directed graphs. We then study the balance problem of general non-unit weighted directed graphs. Numerical experiments for UDQDG are reported. |
| title | Unit Dual Quaternion Directed Graphs, Formation Control and General Weighted Directed Graphs |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2401.05132 |