CDC02-INV2103 In this paper, we provide a graph theoretical framework that allows us to formally define formations of multiple vehicles and the issues arising in graph realizations and unicity and their connections to stability of formations. The notion of graph rigidity is crucial in identifying the shape variables of a formation. This eventually leads to tools for formation stabilization, tacking, and 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-byconstruction graphs by combining smaller rigid subgraphs. This is particularly useful in performing and representing rejoin/split maneuvers of multiple formations in a distributed fashion.
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