  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.
