Symmetry-Based Formation Control on Cycle Graphs Using Dihedral Point Groups
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914188872384512 |
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| author | Martinez, Zamir Zelazo, Daniel |
| author_facet | Martinez, Zamir Zelazo, Daniel |
| contents | This work develops a symmetry-based framework for formation control on cycle graphs using Dihedral point-group constraints. We show that enforcing inter-agent reflection symmetries, together with anchoring a single designated agent to its prescribed mirror axis, is sufficient to realize every $\mathcal{C}_{nv}$-symmetric configuration using only $n-1$ communication links. The resulting control laws have a matrix-weighted Laplacian structure and guarantee exponential convergence to the desired symmetric configuration. Furthermore, we extend the method to enable coordinated maneuvers along a time-varying reference trajectory. Simulation results are provided to support the theoretical analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_06733 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Symmetry-Based Formation Control on Cycle Graphs Using Dihedral Point Groups Martinez, Zamir Zelazo, Daniel Systems and Control Optimization and Control This work develops a symmetry-based framework for formation control on cycle graphs using Dihedral point-group constraints. We show that enforcing inter-agent reflection symmetries, together with anchoring a single designated agent to its prescribed mirror axis, is sufficient to realize every $\mathcal{C}_{nv}$-symmetric configuration using only $n-1$ communication links. The resulting control laws have a matrix-weighted Laplacian structure and guarantee exponential convergence to the desired symmetric configuration. Furthermore, we extend the method to enable coordinated maneuvers along a time-varying reference trajectory. Simulation results are provided to support the theoretical analysis. |
| title | Symmetry-Based Formation Control on Cycle Graphs Using Dihedral Point Groups |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2512.06733 |