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Rigidity and persistence for ensuring shape maintenance of multi‐agent meta‐formations
Author(s) -
Hendrickx Julien M.,
Yu Changbin,
Fidan Barış,
Anderson Brian D. O.
Publication year - 2008
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.14
Subject(s) - rigidity (electromagnetism) , persistence (discontinuity) , generalization , computer science , context (archaeology) , set (abstract data type) , mathematics , engineering , geology , structural engineering , geotechnical engineering , mathematical analysis , paleontology , programming language
This paper treats the problem of merging formations, where the underlying model of a formation is graphical. We first analyze the rigidity and persistence of meta‐formations, which are formations obtained by connecting several rigid or persistent formations. Persistence is a generalization to directed graphs of the undirected notion of rigidity. In the context of moving autonomous agent formations, persistence characterizes the efficacy of a directed structure of unilateral distance constraints seeking to preserve a formation shape. We derive then, for agents evolving in a two‐ or three‐dimensional space, the conditions under which a set of persistent formations can be merged into a persistent meta‐formation, and give the minimal number of interconnections needed for such a merging. We also give conditions for a meta‐formation obtained by merging several persistent formations to be persistent. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society