Aggregated hierarchical sliding-mode control for spherical inverted pendulum

This paper develops methodologies and techniques for modeling and aggregated hierarchical sliding-mode control of a spherical inverted pendulum control system. Lagrangian mechanics is adopted to establish a mathematical model of the system and this model is shown to be consistent with the well-known decoupled model under two special cases. Aggregated hierarchical siding-mode control and backstepping are used to propose a coupled controller so as to maintain the nutation angle at zero and achieve trajectory tracking at the same time. Via Matlab/Simulink, the effectiveness and merit of the proposed controller are exemplified by conducting several simulations on the spherical inverted pendulum system.