A High-Order Fully Actuated System Approach to Control of the 2D Cubli

This study presents a high-order fully actuated (HOFA) system approach to attitude control of 2D Cubli in the presence of disturbances. First, the dynamic model of the underactuated 2D Cubli is derived using the Euler-Lagrange equation. We then leverage the tools and concepts of the recently developed fully actuated approach and transform this model into a HOFA one. Meanwhile, a linear closed-loop system is also obtained to facilitate the design of both the HOFA controller and the disturbance observer. To achieve satisfactory performance, we employ the well-established parameterization design method for the selection and computation of control gains. Finally, we conduct a series of comparative experiments on a self-built Cubli platform to validate the effectiveness of the proposed HOFA controller. Specifically, the proposed HOFA controller improves disturbance rejection by 38.9% and reduces body angular velocity oscillations by 31.9% compared to the traditional LQR-based strategy.