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Toward the Universal Rigidity of General Frameworks

2010/09/07 by Abdo Y. Alfakih, Alfakih, Abdo Y., Nicole Taheri +3
Engineering · Mathematics · #Advanced Materials and Mechanics #FOS: Mathematics #Metric Geometry (math.MG) #Modular Robots and Swarm Intelligence #Optimization and Control (math.OC) #Structural Analysis and Optimization #math.MG #math.OC

paper · pdf · doi:10.48550/arxiv.1009.1185

v2, a revised version of an earlier submission (v1)

openalex publication_date 2010/09/07 · arxiv created 2011/01/06 · arxiv updated 2011/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (G,P) be a bar framework of n vertices in general position in Rd, 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.

Citations

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