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.
Keywords
Laplacian matrixAlgebraic connectivityAlgebraic graph theoryGraphNyquist stability criterionComputer scienceEigenvalues and eigenvectorsTopology (electrical circuits)Graph theoryStability (learning theory)Control theory (sociology)ConnectivityTheoretical computer scienceDistributed computingMathematicsControl (management)Artificial intelligence
Affiliated Institutions
Related Publications
Consensus and Cooperation in Networked Multi-Agent Systems
<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This paper provides a theoretical framework for analysis of consensus algorithms...
Virtual leaders, artificial potentials and coordinated control of groups
We present a framework for coordinated and distributed control of multiple autonomous vehicles using artificial potentials and virtual leaders. Artificial potentials define inte...
Partitioning Sparse Matrices with Eigenvectors of Graphs
The problem of computing a small vertex separator in a graph arises in the context of computing a good ordering for the parallel factorization of sparse, symmetric matrices. An ...
Spectral partitioning works: planar graphs and finite element meshes
Spectral partitioning methods use the Fiedler vector-the eigenvector of the second-smallest eigenvalue of the Laplacian matrix-to find a small separator of a graph. These method...
Distributed structural stabilization and tracking for formations of dynamic multi-agents
We provide a theoretical framework that consists of graph theoretical and Lyapunov-based approaches to stability analysis and distributed control of multi-agent formations. This...
Publication Info
- Year
- 2004
- Type
- article
- Volume
- 49
- Issue
- 9
- Pages
- 1465-1476
- Citations
- 4539
- Access
- Closed
External Links
Social Impact
Altmetric
PlumX Metrics
Social media, news, blog, policy document mentions
Citation Metrics
4539
OpenAlex
Cite This
J.A. Fax,
Richard M. Murray
(2004).
Information Flow and Cooperative Control of Vehicle Formations.
IEEE Transactions on Automatic Control
, 49
(9)
, 1465-1476.
https://doi.org/10.1109/tac.2004.834433
Identifiers
- DOI
- 10.1109/tac.2004.834433