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Formation Reorganization by Primitive Operations on Directed Graphs (2008)
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BibTeX
@MISC{Hendrickx08formationreorganization,
author = {Julien M. Hendrickx and Barıs Fidan and Changbin (brad) Yu and Brian D. O. Anderson and Vincent D. Blondel},
title = {Formation Reorganization by Primitive Operations on Directed Graphs},
year = {2008}
}
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Abstract
In this paper, we study the construction and transformation of 2-D persistent graphs. Persistence is a generalization to directed graphs of the undirected notion of rigidity. Both notions are currently being used in various studies on coordination and control of autonomous multiagent formations. In the context of mobile autonomous agent formations, persistence characterizes the efficacy of a directed formation structure with unilateral distance constraints seeking to preserve the shape of the formation. Analogously to the powerful results about Henneberg sequences in minimal rigidity theory, we propose different types of directed graph operations allowing one to sequentially build any minimally persistent graph (i.e., persistent graph with a minimal number of edges for a given number of vertices), each intermediate graph being also minimally persistent. We also consider the more generic problem of obtaining one minimally persistent graph from another, which corresponds to the online reorganization of the sensing and control architecture of an autonomous agent formation. We prove that we can obtain any minimally persistent formation from any other one by a sequence of elementary local operations such that minimal persistence is preserved throughout the reorganization process. Finally, we briefly explore how such transformations can be performed in a decentralized way.
Keyphrases
directed graph formation reorganization persistent graph primitive operation autonomous agent formation various study powerful result henneberg sequence elementary local operation autonomous multiagent formation intermediate graph different type control architecture minimal rigidity theory decentralized way 2-d persistent graph mobile autonomous agent formation unilateral distance constraint online reorganization undirected notion generic problem minimal persistence directed formation structure directed graph operation reorganization process multiagent formation index term graph minimal number persistent formation
