Abstract
A bar framework determined by a finite graph $$G$$G and a configuration $$\mathbf{p =(p_1,\ldots , p_n) }$$p=(p1,?,pn) in $$\mathbb {R}^d$$Rd is universally rigid if it is rigid in any $$\mathbb {R}^D \supset \mathbb {R}^d$$RD?Rd. We provide a characterization of universal rigidity for any graph $$G$$G and any configuration $$\mathbf{p}$$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.
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