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Neural Integral Backstepping Hierarchical Sliding Mode Control for a Ridable Ballbot Under Uncertainties and Input Saturation

This article proposes a novel adaptive backstepping hierarchical sliding mode control with balance and transfer for a ridable ballbot. The algorithm is applied to the dynamics of coupling two vertical planes. The dynamic model is a multiple-input–multiple-output underactuated system. Based on the backstepping and hierarchical sliding mode schemes, a robust nonlinear control law is obtained to govern the balance and transfer of the ridable ballbot; this scheme considers input constraints as well as matched and mismatched uncertainties. The influence of actuator saturation is examined by proposing an auxiliary system. The stability of the whole system is guaranteed via Lyapunov theory and Barbalat’s lemma, which shows that the switching gains are limited by the upper bound of the matched uncertainty. An adaptive law is proposed to estimate the matched uncertainty using radial bias function networks. As a result, the robustness is enhanced, and the constraints of the switching gains on the matched uncertainty can be relaxed. The stabilizing and tracking problems of the ridable ballbot are investigated through comparative simulations. The results demonstrate the effectiveness and robustness of the proposed control algorithm in the presence of parameter variations, external disturbances, and input saturation.