Dynamic balance and motion control for wheeled inverted pendulum vehicle via hierarchical sliding mode approach

Abstract

Dynamic balance and motion control for a class of underactuated wheeled inverted pendulum vehicles that are inherent unstable are investigated in this study. The control objective is to stable the posture of the vehicle platform (longitudinal and rotational position/velocity) as well as hold upright position of the pendulum (tilt angle stability), only with two control inputs generated by the left and right motors. The overall dynamic system is separated into two decoupled subsystems: one is a one-dimensional fully actuated subsystem while the other is a two-dimensional underactuated subsystem. A new hierarchical sliding mode control methodology is first developed to resolve the underactuated problem of this kind of unstable vehicles. The first layer sliding mode surfaces are established upon tilt angle and longitudinal displacement of the vehicle body, respectively; while the second layer sliding mode surface is constructed by the first layer sliding mode surfaces. Consequently, the total control law is deduced, and then the asymptotic stabilities for the overall closed-loop control system are addressed via Lyapunov stability theorem and Barbalat’s Lemma. Numerical simulations illustrate the effectiveness of the proposed control approaches and methodologies.