Adaptive Hierarchical Sliding Mode Control for Full Nonlinear Dynamics of Uncertain Ridable Ballbots under Input Saturation

This article proposes a nonlinear adaptive controller based on a hierarchical sliding mode control framework to stabilize the operation of a ridable ballbot based on the full nonlinear dynamics (FND). The FND of ballbots is a multiple-input-multiple-output underactuated system, in which the input matrix is non-invertible. By applying a novel approach to transform the FND into two subsystems, the invertibility of the input matrix of these subsystems can be guaranteed. Thus, a hierarchical sliding mode control (HSMC) scheme can be applied to control the ridable ballbot system by stabilizing these subsystems. Moreover, we propose new adaptive laws to enhance the robustness of the HSMC to deal with the effects of parameter variations and exogenous disturbances on the modeled dynamics. Chattering and actuator saturation phenomena are also reduced or avoided under the proposed controller. Comparative simulations are conducted to demonstrate the merit features of the proposed approach and the robustness of the developed control algorithm.