Robustness issues with undirected formations

It is shown for any rigidity-based, undirected triangular formation of the type studied in [1], that if neighboring agents in the formation have slightly different understandings of what the desired distance between them is suppose to be, then almost for certain, the trajectory of the resulting distorted but rigid formation will converge exponentially fast to a closed orbit in ℝ
²
which is traversed periodically at a single sinusoidal frequency.