  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, yield to be a special 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, as well as promoting
the integration of structure and control design.
