Dynamics and control of clustered tensegrity systems

This paper presents the formulations of nonlinear and linearized statics, dynamics, and control for any clustered tensegrity system (CTS). Based on the Lagrangian method and FEM assumptions, the nonlinear clustered tensegrity dynamics with and without constraints are first derived. It is shown that the traditional tensegrity system (TTS), whose node to node strings are individual ones, yields to be a particular case of the CTS. Then, equilibrium equations of the CTS in three standard forms (in terms of nodal coordinate, force density, and force vector) and the compatibility equation are given. Moreover, the linearized dynamics and modal analysis of the CTS with and without constraints are also derived. We also present a nonlinear shape control law for the control of any CTS. The control turns out to be a linear algebra problem in terms of the control variable, which is the force densities in the strings. The statics, dynamics, and control examples are carefully selected to demonstrate the developed principles. The presented approaches can boost the comprehensive studies of the statics, dynamics, and control for any CTS or TTS, as well as promote the integration of structure and control design.