Generic Global Rigidity

By R. Connelly. Discrete & Computational Geometry, 2005

463 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computer Graphics and Computer-Aided Design, Mechanical Engineering

View Paper: https://www.semanticscholar.org/paper/0f75831d659278e7889b22dde55f0dfd4339bbad

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In Civil and Structural Engineering

In Computer Graphics and Computer-Aided Design

In Mechanical Engineering

Citations in the corpus

Rigid graph control architectures for autonomous formations (2008, background): “DECEMBER 2008 « IEEE CONTROL SYSTEMS MAGAZINE 55 Global Rigidity Characterization Anice characterization of global rigidity [22] is available for twodimensional formations and their associated graphs.”
Bearing Rigidity and Almost Global Bearing-Only Formation Stabilization (2014, background): “In order to prove Theorem 8 and Corollary 1, we need first introduce some concepts and results in the distance rigidity theory [22], [23].”
Anchor-Free Distributed Localization in Sensor Networks (2003, background): “A graph with specified edge lengths which has a unique embedding is called globally rigid [4, 12], a variation on the well-studied concepts in rigidity theory [5, 10, 9].”
Affine Formation Maneuver Control of Multiagent Systems (2018, background): “We next review some necessary notions in the distance rigidity theory [23]– [25].”
Advanced form-finding of tensegrity structures (2010, background): “prestress levels [17–19,25].”
Localization Algorithms and Strategies for Wireless Sensor Networks: Monitoring and Surveillance Techniques for Target Tracking (2009, background): “The remaining open case, d = 2, was settled by the following result, which incorporated earlier results from (Connelly, 2005; Hendrickson, 1992) and a new inductive construction for the family of 3-connected redundantly rigid graphs (see in the section on inductive constructions).”
Advanced form-finding for cable-strut structures (2010, background): “The Cable dome structures first proposed by Geiger et al. (1986) have been developed in recent years due to their innovative forms, lightweight and deployability.”
Connected rigidity matroids and unique realizations of graphs (2005, unknown): “Following Connelly[4], we say that a graphG is globally rigid in R if every generic realization of G in R is a unique realization.”
The Cricket indoor location system (2005, background): “Connelly [19] proved that these two properties are insufficient in 3D: they do not imply generic global rigidity of a 3D graph.”
Mobile-assisted localization in wireless sensor networks (2005, background): “Connelly [17] proved that these two properties are insufficient in 3D: they do not imply generic global rigidity of a 3D graph.”
Notes on the Rigidity of Graphs (2007, methodology): “Connelly’s proof is less elementary than our proof of Theorem 5.5.”
Wireless sensor network localization techniques (2007, background): “A particular graph property associated with unique localizability of sensor networks is global rigidity [106,108,109].”
Rigidity, computation, and randomization in network localization (2004, background): “Theorem 7 ([13], [18]): If a graph with more than d + 1 vertices is generically globally rigid in d-space, then G is redundantly rigid and at least d+1 connected.”
A Theory of Network Localization (2006, background): “, solvable) in spaces of all dimensions [14], [21].”