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

•Inclusion of the remaining DOF in the H∞H∞ control problem for underactuated systems.•We ensure the stabilization of the remaining DOF and regulation of controlled DOF.•We allow adjusting the time-derivative of the remaining DOF in a desired value.•A new method for tuning the nonlinear H∞H∞ control law for mechanical systems.•Application of the proposed controller to a real two-wheeled self-balanced vehicle.

A nonlinear H∞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) (φ̇=0rad/s), or at least its velocity (mechanical equilibrium) (φ̇=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∞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.