Robust integral backstepping hierarchical sliding mode controller for a ballbot system

摘要

A ballbot is a mobile robot with the ability to simultaneously move and balance on a spherical ball. In this study, we proposed control algorithms to stabilize the decoupled dynamics of a ballbot, which has three orthogonal planes. The uncertainties are considered in the modeled dynamics. The operations of the whole system are separately controlled through stabilization on these planes. By using systematic backstepping techniques, a robust nonlinear controller based on a hierarchical sliding mode control is proposed to achieve balance and movement in the vertical planes. The closed-loop system stability is obtained by using the Lyapunov stability criterion and Barbalat's lemma. The robustness of the proposed algorithm in rejecting unknown lumped perturbations, which is a well-known characteristic of sliding mode control, is evaluated. A proportional-integral-derivative feedforward controller is proposed to control the heading in the horizontal plane. Several experiments were performed on a real system to validate the system design, and demonstrate the robustness of the proposed control algorithm for an underactuated mechanical system.