  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.
