72 citations · 250 across the 57 of their papers we have counts for
5 papers · 1 filter
A geometric view of formation control with application to directed sensing
Louis Theran, Daniel Zelazo, Jessica Sidman
We propose a geometric approach to distance-based formation control modeled on a minimum-norm lifting of Riemannian gradient descent in edge-space to node-space. This yields a unif…
Uniquely realizable crystalline structures
Sean Dewar, Bernd Schulze, Shin-ichi Tanigawa +1
We construct infinite periodic versions of the stress matrix and establish sufficient conditions for periodic tensegrity frameworks to be globally rigid in in the ca…
Linearizing Algebraic Matroids
Zvi Rosen, Jessica Sidman, Louis Theran
Although algebraic matroids were discovered in the 1930s, interest in them was largely dormant until their recent use in applications of algebraic geometry. Because nonlinear algeb…
Higher Order Rigidity and Energy
Steven J. Gortler, Miranda Holmes-Cerfon, Louis Theran
In this paper, we revisit the notion of higher-order rigidity of a bar-and-joint framework. In particular, we provide a link between the rigidity properties of a framework, and the…
Equilibrium stresses in frameworks via symmetric averaging
Cameron Millar, Bernd Schulze, Louis Theran
For a bar-joint framework , a subgroup of the automorphism group of , and a subgroup of the orthogonal group isomorphic to , we introduce a symmetric averaging map…