Recently, The Land, Air and Space Robotics (LASR) Laboratory has demonstrated a state-of-the-art proximity operations test bed that will revolutionize the concept of portable space systems simulation. The Holonomic Omni-directional Motion Emulation Robot (HOMER) permits in nite, un-tethered circumnavigations of one object by another. To allow this platform to operate at the desired performance, an appropriate implementation of feedback control is essential. The dynamic model is derived and presented using a Lagrangian approach. A Lyapunov method is used to form proportional-derivative (PD) and proportional-integral-derivative (PID) feedback controllers. These controllers are validated with computer-based simulation and compared through experimental results. Finally, a frequency analysis is performed in an effort to identify the bandwidth of the system and provide a better understanding of the expected system performance for reference motions containing harmonic perturbations.