Information Flow and Cooperative Control of Vehicle Formations

TLDR

Algebraic graph theory tools model the communication network and link its topology to formation stability. The study addresses cooperative vehicle control by proving a Nyquist criterion based on graph Laplacian eigenvalues and proposing a decentralized information exchange method to coordinate shared tasks. The authors develop a dynamical system that supplies each vehicle with a common reference, using the Nyquist criterion and decentralized exchange to realize cooperative motion. They prove a separation principle decomposing formation stability into graph‑based information flow and individual vehicle stability, demonstrating that robust information flow enables tight formation control even with limited intervehicle communication.

Abstract

We consider the problem of cooperation among a collection of vehicles performing a shared task using intervehicle communication to coordinate their actions. Tools from algebraic graph theory prove useful in modeling the communication network and relating its topology to formation stability. We prove a Nyquist criterion that uses the eigenvalues of the graph Laplacian matrix to determine the effect of the communication topology on formation stability. We also propose a method for decentralized information exchange between vehicles. This approach realizes a dynamical system that supplies each vehicle with a common reference to be used for cooperative motion. We prove a separation principle that decomposes formation stability into two components: Stability of this is achieved information flow for the given graph and stability of an individual vehicle for the given controller. The information flow can thus be rendered highly robust to changes in the graph, enabling tight formation control despite limitations in intervehicle communication capability.