Zero-dynamics-based adaptive sliding mode control for a wheeled inverted pendulum with parametric friction and uncertain dynamics compensation

In this paper, we propose a novel control methodology based on zero-dynamics theory for a class of wheeled inverted pendulum (WIP) vehicles, which is efficient even in the presence of uncertain system frictions and dynamics parameters. The control schemes are elegantly constructed so that the WIP vehicle can successfully implement stabilizing of the posture (longitudinal and rotational movements), as well as hold the upright position of the vehicle body (tilt angle stability), only by the two control inputs with the aid of the design approach of zero-dynamics. In particular, the dynamics uncertainties, especially the friction effects, would deteriorate the control performance severely in practice. Therefore, we employ adaptive laws for the design parameters of zero-dynamics subsystem and uncertain coefficients of parametric frictions and dynamics. Consequently, the estimated frictions and dynamics are compensated through feedforward to obtain better control performance. To enhance the robustness of the system against parameter variations and external disturbances, sliding mode control techniques are applied to derive the specific algorithms, and then the closed-loop systems are proven to be globally asymptotically stable by Lyapunov techniques and LaSalle’s invariance theorem. In addition, simulation studies have been performed to demonstrate the feasibility and effectiveness of the proposed strategies, which illuminate the promising practical application potentiality of the designed WIP vehicle control system.