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 3-D Cubli 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 3-D 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 final controller is then developed based on the disturbance observer and the baseline controller. The stability of the overall 3-D Cubli system has been established rigorously. The proposed scheme exhibits improved performance compared to the linearization-based linear quadratic regulator 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 3-D Cubli platform.