Journal
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
Volume 49, Issue 9, Pages 1465-1476Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2004.834433
Keywords
cooperative control; graph theory; Laplacian; multivehicle control; stability
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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 the 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.
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