Udwadia-Kalaba Equation Based Adaptive Robust Control for Two-wheeled Inverted Pendulum System: Underactuation and Uncertainty

A new adaptive robust control method based on Udwadia-Kalaba(U-K) approach which can be applied to the underactuated system is designed and used to two-wheeled inverted pendulum system in this paper. We separate this typical underactuated system into two subsystems(forward subsystem and yaw subsystem), which are fully underactuated and actuated. For these different subsystems, we use different control methods. We apply an adaptive robust control method which has been proved many times to the fully actuated subsystem. Based on this adaptive robust method, a new control strategy can be redesigned and applied to the underactuated subsystem by modifying the adaptive law and other things. This adaptive robust control with a leakage-type adaptive law could guarantee the uniform boundedness and uniform ultimate boundedness of the system. Finally, the simulation is executed to demonstrate the advantage and simplicity of the proposed method.