Distributed Multi-agent Coordination over Cellular Sheaves
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arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910903255957504 |
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| author | Hanks, Tyler Riess, Hans Cohen, Samuel Gross, Trevor Hale, Matthew Fairbanks, James |
| author_facet | Hanks, Tyler Riess, Hans Cohen, Samuel Gross, Trevor Hale, Matthew Fairbanks, James |
| contents | Techniques for coordination of multi-agent systems are vast and varied, often utilizing purpose-built solvers or controllers with tight coupling to the types of systems involved or the coordination goal. In this paper, we introduce a general unified framework for heterogeneous multi-agent coordination using the language of cellular sheaves and nonlinear sheaf Laplacians, which are generalizations of graphs and graph Laplacians. Specifically, we introduce the concept of a nonlinear homological program encompassing a choice of cellular sheaf on an undirected graph, nonlinear edge potential functions, and constrained convex node objectives, which constitutes a standard form for a wide class of coordination problems. We use the alternating direction method of multipliers to derive a distributed optimization algorithm for solving these nonlinear homological programs. To demonstrate the applicability of this framework, we show how heterogeneous coordination goals including combinations of consensus, formation, and flocking can be formulated as nonlinear homological programs and provide numerical simulations showing the efficacy of our distributed solution algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_02049 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Distributed Multi-agent Coordination over Cellular Sheaves Hanks, Tyler Riess, Hans Cohen, Samuel Gross, Trevor Hale, Matthew Fairbanks, James Optimization and Control Multiagent Systems Algebraic Topology 93A16, 93B45, 55N30 Techniques for coordination of multi-agent systems are vast and varied, often utilizing purpose-built solvers or controllers with tight coupling to the types of systems involved or the coordination goal. In this paper, we introduce a general unified framework for heterogeneous multi-agent coordination using the language of cellular sheaves and nonlinear sheaf Laplacians, which are generalizations of graphs and graph Laplacians. Specifically, we introduce the concept of a nonlinear homological program encompassing a choice of cellular sheaf on an undirected graph, nonlinear edge potential functions, and constrained convex node objectives, which constitutes a standard form for a wide class of coordination problems. We use the alternating direction method of multipliers to derive a distributed optimization algorithm for solving these nonlinear homological programs. To demonstrate the applicability of this framework, we show how heterogeneous coordination goals including combinations of consensus, formation, and flocking can be formulated as nonlinear homological programs and provide numerical simulations showing the efficacy of our distributed solution algorithm. |
| title | Distributed Multi-agent Coordination over Cellular Sheaves |
| topic | Optimization and Control Multiagent Systems Algebraic Topology 93A16, 93B45, 55N30 |
| url | https://arxiv.org/abs/2504.02049 |