Toward the Universal Rigidity of General Frameworks

Let (G,P) be a bar framework of n vertices in general position in R^d, d <= n-1, where G is a (d+1)-lateration graph. In this paper, we present a constructive proof that (G,P) admits a positive semi-definite stress matrix with rank n-d-1. We also prove a similar result for a sensor network where...

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Bibliographic Details
Published inarXiv.org
Main Authors Alfakih, Abdo Y, Taheri, Nicole, Ye, Yinyu
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 06.01.2011
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Mathematical analysis
Matrix methods
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Summary:Let (G,P) be a bar framework of n vertices in general position in R^d, d <= n-1, where G is a (d+1)-lateration graph. In this paper, we present a constructive proof that (G,P) admits a positive semi-definite stress matrix with rank n-d-1. We also prove a similar result for a sensor network where the graph consists of m(>= d+1) anchors.
ISSN:2331-8422