We develop a rigidity theory for bar-joint frameworks in Euclidean d-space in which specified classes of edges are allowed to change length in a coordinated fashion that requires differences of lengths to be preserved within each class. Rigidity for these coordinated frameworks is a generic property, and we characterize the rigid graphs in terms of redundant rigidity in the standard d-dimensional rigidity matroid. We also interpret our main results in terms of matroid unions.
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Schulze et al. (2022) studied this question.
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