  This paper proposes a model-based approach to control the shape of a
tensegrity system by driving its node position locations. The nonlinear
dynamics of the tensegrity system is used to regulate position, velocity, and
acceleration to the specified reference trajectory. State feedback control
design is used to obtain the solution for the control variable as a linear
programming problem. Shape control for the gyroscopic tensegrity systems is
discussed, and it is observed that these systems increase the reachable space
for the structure by providing independent control over certain rotational
degrees of freedom. Disturbance rejection of the tensegrity system is further
studied in the paper. A methodology to calculate the control gains to bound the
errors for five different types of problems is provided. The formulation uses a
Linear Matrix Inequality (LMI) approach to stipulate the desired performance
bounds on the error for $\mathcal{H}_\infty$, generalized $\mathcal{H}_2$, LQR,
covariance control and stabilizing control problem. A high degree of freedom
tensegrity $T_2D_1$ robotic arm is used as an example to show the efficacy of
the formulation.
