{"ID":2831971,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.06733","arxiv_id":"2512.06733","title":"Symmetry-Based Formation Control on Cycle Graphs Using Dihedral Point Groups","abstract":"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.","short_abstract":"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 $\\mathcal{C}_{nv}$-symmetr...","url_abs":"https://arxiv.org/abs/2512.06733","url_pdf":"https://arxiv.org/pdf/2512.06733v2","authors":"[\"Zamir Martinez\",\"Daniel Zelazo\"]","published":"2025-12-07T08:57:41Z","proceeding":"eess.SY","tasks":"[\"eess.SY\",\"math.OC\"]","methods":"[]","has_code":false}