Rigidity and persistence for ensuring shape maintenance of multi‐agent meta‐formations
Julien M. Hendrickx, Changbin Brad Yu, Barış Fi̇dan, Brian D. O. Anderson · Asian Journal of Control · 2008
Abstract 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