A geometric view of formation control with application to directed sensing
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914183005601792 |
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| author | Theran, Louis Zelazo, Daniel Sidman, Jessica |
| author_facet | Theran, Louis Zelazo, Daniel Sidman, Jessica |
| contents | We propose a geometric approach to distance-based formation control modeled on a minimum-norm lifting of Riemannian gradient descent in edge-space to node-space. This yields a unified family of controllers, including the classical gradient controller and its directed variant. For the directed case, we give a simple numerical test for local convergence that applies to any directed graph and target. We show that persistence is neither necessary nor sufficient for local convergence of our directed controller and propose an alternative that is necessary and more easily checked. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_06195 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A geometric view of formation control with application to directed sensing Theran, Louis Zelazo, Daniel Sidman, Jessica Optimization and Control Metric Geometry We propose a geometric approach to distance-based formation control modeled on a minimum-norm lifting of Riemannian gradient descent in edge-space to node-space. This yields a unified family of controllers, including the classical gradient controller and its directed variant. For the directed case, we give a simple numerical test for local convergence that applies to any directed graph and target. We show that persistence is neither necessary nor sufficient for local convergence of our directed controller and propose an alternative that is necessary and more easily checked. |
| title | A geometric view of formation control with application to directed sensing |
| topic | Optimization and Control Metric Geometry |
| url | https://arxiv.org/abs/2512.06195 |