Distributed Multi-agent Coordination over Cellular Sheaves

2025-04-02

AI Summary

Addressing the challenge of unifying consensus, formation control, and flocking in heterogeneous multi-agent systems, this paper proposes a distributed coordination framework based on cellular sheaves. Methodologically, it integrates cellular sheaf theory, distributed convex optimization, the alternating direction method of multipliers (ADMM), and graph signal processing. The key contribution is the first formulation of a nonlinear sheaf Laplacian operator and a homological programming model, generalizing the classical graph Laplacian to nonlinear sheaf structures; this enables unified modeling of coupled objectives and decoupled constraint optimization. Numerical experiments demonstrate that the proposed algorithm achieves strong convergence, robustness, and scalability in heterogeneous networks. The framework provides a generic, analyzable, and scalable paradigm for solving diverse cooperative control tasks under a unified theoretical foundation.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Multiagent Systems: Coordination and Collaboration
• Search and Optimization: Distributed Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Federated Web and WoT systems, including distributed, federated and edge-based data processing
• Economics, Online Markets and Human Computation: The sharing economy

Abstract

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. We use the alternating direction method of multipliers to derive a distributed optimization algorithm for solving these nonlinear homological programs. To demonstrate the wide applicability of this framework, we show how hybrid 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.

Problem

• General framework for heterogeneous multi-agent coordination
• Nonlinear homological programs for hybrid coordination goals
• Distributed optimization algorithm using ADMM

Innovation

• General framework using cellular sheaves
• Nonlinear homological programs for coordination
• Distributed optimization via ADMM algorithm