In this paper the problem of swing-up control of an under-actuated, three-link robot gymnast (Robogymnast) is discussed. Robogymnast mimics the human acrobat who hangs from a high bar and tries to swing-up to an upside-down position with his/her hands still on the bar. Unlike human acrobats, Robogymnast’s hands are firmly attached to a freely rotating high bar mounted on ball bearings. Although this helps during the swing-up phase, it poses a great challenge to balancing the robot at the upright position.