In this paper, a high-order disturbance observer for a class of underactuated robotic systems with mismatched uncertainties is proposed. In order to improve its estimation performance, a choice method of optimal gain matrices of the high-order disturbance observer is obtained as the solution of an optimization problem. A high-order disturbance observer based sliding mode control method is also designed for this class of underactuated robotic system with mismatched disturbance. The stabilities of both the disturbance observer and the controlled closed-loop system are proved by the Lyapunov theorem. Simulations on a benchmark Acrobot system demonstrate the efficiency of proposed approaches.

There has been increasing interest in a type of underactuated mechanical systems, mobile-wheeled inverted-pendulum (MWIP) models, which are widely used in the field of autonomous robotics and intelligent vehicles. Robust-velocity-tracking problem of the MWIP systems is investigated in this study. In the velocity-control problem, model uncertainties accompany uncertain equilibriums, which make the controller design become more difficult. Two sliding-mode-control (SMC) methods are proposed for the systems, both of which are capable of handling both parameter uncertainties and external disturbances. The asymptotical stabilities of the corresponding closed-loop systems are achieved through the selection of sliding-surface parameters, which are based on some rules. There is still a steady tracking error when the first SMC controller is used. By assuming a novel sliding surface, the second SMC controller is designed to solve this problem. The effectiveness of the proposed methods is finally confirmed by the numerical simulations.

In this paper, a novel high-order disturbance observer (HODO) for the Mobile Wheeled Inverted Pendulum (MWIP) system is firstly proposed. Based on a choice method of optimal gain matrices, the estimation accuracy of the HODO can be improved. Combining the proposed HODO and sliding mode control (SMC), a new control strategy is designed for the balance and speed control of the MWIP system. The boundness of the estimation error of HODO is proved and the stability of the closed-loop control system is achieved through the appropriate selection of sliding surface coefficients. The effectiveness of all proposed methods is verified by experiments on a real MWIP system.