A High-Order Fully Actuated System Approach to Attitude Control of 3-D Cubli

The Cubli is an interesting underactuated mechatronics system that can balance on one of its corners or edges by applying controlled torques to the reaction wheels mounted on its three faces. This study presents a high-order fully actuated (HOFA) system approach to attitude control of 3D Cublis with additive disturbances. First, by adopting the concepts and tools from the recently developed HOFA system theory, we transform the system model of the Cubli into a HOFA one. We then leverage the latter model that has the full actuation characteristic to design a baseline controller to eliminate the nonlinearities inherent in the 3D Cubli system, thereby resulting in linear dynamics with additive nonlinear terms. Second, a nonlinear observer is developed to estimate the additive system disturbance in real time. The estimated disturbance is then utilized to improve the effectiveness of the baseline controller. The rigorous stability of the overall 3D Cubli system has been established. The proposed scheme exhibits improved performance compared to the linearization-based LQR strategy and the backstepping strategy in numerical simulations. The effectiveness of the proposed framework has also been extensively validated in hardware experiments on a self-built 3D Cubli platform.