Gyroscopically Stabilized Robot: Balance and Tracking
  The single wheel, gyroscopically stabilized robot - Gyrover, is a dynamically stable but statically unstable, underactuated system. In this paper, based on the dynamic model of the robot, we investigate two classes of nonholonomic constraints associated with the system. Then, based on the backstepping technology, we propose a control law for balance control of Gyrover. Next, through transferring the systems states from Cartesian coordinate to polar coordinate, control laws for point-to-point control and line tracking in Cartesian space are provided. 
Yongsheng Ou & Yangsheng Xu