This paper presents the design, analysis, and testing of a fully actuated modular spherical tensegrity robot for co-robotic and space exploration applications. Robots built from tensegrity structures (composed of pure tensile and compression elements) have many potential benefits including high robustness through redundancy, many degrees-of-freedom in movement and flexible design. However, to take full advantage of these properties, a significant fraction of the tensile elements should be active, leading to a potential increase in complexity, messy cable, and power routing systems and increased design difficulty. Here, we describe an elegant solution to a fully actuated tensegrity robot: The TT-3 (version 3) tensegrity robot, developed at UC Berkeley, in collaboration with NASA Ames, is a lightweight, low cost, modular, and rapidly prototyped spherical tensegrity robot. This robot is based on a ball-shaped six-bar tensegrity structure and features a unique modular rod-centered distributed actuation and control architecture. This paper presents the novel mechanism design, architecture, and simulations of TT-3, an untethered, fully actuated cable-driven six-bar spherical tensegrity robot. Furthermore, this paper discusses the controls and preliminary testing performed to observe the system's behavior and performance and is evaluated against previous models of tensegrity robots developed at UC Berkeley and elsewhere.