Iterative Universal Rigidity

Abstract

A bar framework determined by a finite graph $G$ and configuration $\mathbf{p}$ in $d$ space is universally rigid if it is rigid in any ${\mathbb{R}}^D\supset {\mathbb{R}}^d$. We provide a characterization of universally rigidity for any graph $G$ and any configuration $\mathbf{p}$ in terms of a sequence of affine subsets of the space of configurations. This corresponds to a facial reduction process for closed finite dimensional convex cones.

41 pages, 12 figures

References in corpus (2)

• Localization from Incomplete Noisy Distance Measurements
• The Gram dimension of a graph

Cited by in corpus (1)

• On Farkas Lemma and Dimensional Rigidity of Bar Frameworks