Graph rigidity and distributed formation stabilization of multi-vehicle systems

We provide a graph theoretical framework that allows us to formally define formations of multiple vehicles and the issues arising in uniqueness of graph realizations and its connection to stability of formations. The notion of graph rigidity is crucial in identifying the shape variables of a formati...

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Bibliographic Details
Published inProceedings of the 41st IEEE Conference on Decision and Control, 2002 Vol. 3; pp. 2965 - 2971 vol.3
Main Authors Olfati-Saber, R., Murray, R.M.
Format Conference Proceeding
LanguageEnglish
Published IEEE 2002
Subjects
Algebra
Automatic control
Biological control systems
Biology
Computer science
Control systems
Control theory
Shape
Stability
Unmanned aerial vehicles
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ISBN0780375165
9780780375161
ISSN0191-2216
DOI10.1109/CDC.2002.1184307

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Summary:We provide a graph theoretical framework that allows us to formally define formations of multiple vehicles and the issues arising in uniqueness of graph realizations and its connection to stability of formations. The notion of graph rigidity is crucial in identifying the shape variables of a formation and an appropriate potential function associated with the formation. This allows formulation of meaningful optimization or nonlinear control problems for formation stabilization/tacking, in addition to formal representation of split, rejoin, and reconfiguration maneuvers for multi-vehicle formations. We introduce an algebra that consists of performing some basic operations on graphs which allow creation of larger rigid-by-construction graphs by combining smaller rigid subgraphs. This is particularly useful in performing and representing rejoin/split maneuvers of multiple formations in a distributed fashion.
ISBN:0780375165
9780780375161
ISSN:0191-2216
DOI:10.1109/CDC.2002.1184307