Constructing universally rigid tensegrity frameworks with application in multiagent formation control

Rigidity graph theory has found broad applications in engineering, architecture, biology, and chemistry, while systematic and computationally tractable construction of rigid frameworks is still a challenging task. In this paper, starting from any given configuration in general positions, we show how to construct a universally rigid tensegrity framework by looking into the kernel of the tensegrity framework's stress matrix. As one application, we show how to stabilize a formation of mobile agents by assigning a universally rigid virtual tensegrity framework for the formation and then design distributed controllers based on the forces determined by the stresses of the edges. Such formation controllers are especially useful when one needs to satisfy formation constraints in the form of strict upper or lower bounds on interagent distances arising from tethered robots.