A Fully Actuated System Approach to Control of the 3D Cubli: Theory and Experiments

The 3D Cubli is an interesting underactuated mechatronics system that has reaction wheels mounted on three of its faces and can balance on its corner or edge by applying controlled torques to the reaction wheels. Control of the 3D Cubli has attracted much attention in the literature, yet remains challenging due to strong nonlinearity and coupling inherent in the system, as well as adverse effects from external disturbances, unknown friction and other unmodeled dynamics that further intensify the difficulty of regulating system attitude. To address the above issues, this paper is concerned with high-order fully actuated (HOFA) system approach to control of the 3D Cubli. First, by adopting the concepts and tools from the recently developed fully actuated system approach, we transform the system dynamics of the Cubli into a nonlinear HOFA model. We leverage the full actuation property of the latter model to design a baseline controller to eliminate the nonlinearities inherent in the Cubli system. Second, a nonlinear observer is developed to estimate the additive system disturbance in real time. The estimated disturbance is then used to enhance the performance of the baseline controller. The stability of the closed-loop system has been rigorously established. Compared to the linearization-based LQR strategy, the proposed framework exhibits significantly better performance in hardware experiments that were conducted on a self-built 3D Cubli platform by the authors.