Distributed Multi-agent Coordination over Cellular Sheaves

Fuente: arXiv
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Autori principali: Hanks, Tyler, Riess, Hans, Cohen, Samuel, Gross, Trevor, Hale, Matthew, Fairbanks, James
Natura: Preprint
Pubblicazione: 2025
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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