The ability for robots in space to carry out coordinated tasks such as assembly requires a significant level of dexterity to optimally manipulate a wide array of objects. A baseline for optimality, the tensegrity structure in the human arm features a continuous network of tendons that uniformly distribute external forces among the entire internal tension network. This research lays the groundwork for an optimally controlled tensegrity robotic arm through dynamic modeling and LQR control realization.