Graph Laplacians and Stabilization of Vehicle Formations
J. Alexander Fax and Richard M. Murray
CDS Technical Report 01-007.
2002 IFAC World Congress
Control of vehicle formations has emerged as a topic of significant interest to the controls
community. In this paper, we merge tools from graph theory and control theory to derive
stability criteria for formation stabilization. The interconnection between vehicles (i.e., which
vehicles are sensed by other vehicles) is modeled as a graph, and the eigenvalues of the Laplacian
matrix of the graph are used in stating a Nyquist-like stability criterion for vehicle formations.
The location of the Laplacian eigenvalues can be correlated to the graph structure, and therefore
used to identify desirable and undesirable formation interconnection topologies.
Preprint
(11 pages, PDF, 138K)
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Richard Murray
(murray@cds. caltech.edu)