Two-wheeled self-balanced pendulum workspace improvement via underactuated robust nonlinear control

Abstract A nonlinear H ∞ controller is designed and applied for two-wheeled self-balanced vehicles, which are underactuated mechanical systems with input coupling. The main objective is, in the presence of exogenous disturbances, to ensure that the inclination angle of the pendulum ( controlled DOF) is led to the upper vertical position, while the angular velocity of the wheels (the time-derivative of the remaining DOF) can be set in a desired reference value. Thus, the angular position of the wheels ( remaining DOF) is driven to steady state, i.e., it is maintained stabilized (static equilibrium) ( φ = 0 rad / s ), or at least its velocity (mechanical equilibrium) ( φ = const . rad / s ). The proposed controller considers the whole dynamics of the system into its structure, ensuring that the overall system is closed-loop stable. Furthermore, an improvement of the nonlinear H ∞ control tuning method for mechanical systems is developed. Experimental results are carried out with a real two-wheeled vehicle in the presence of external disturbances, unmodeled dynamics and from extreme initial conditions.