Adaptive robust control for the corner balancing Cubli system with uncertainties

Abstract

The Cubli is a cube that can balance on its edge or corner by rotating inertia wheels. It is a typical underactuated mechanical system, and has 6 degrees of freedom when balancing on its corner. In this paper, an adaptive robust control is presented to balance the uncertain Cubli system on its corner. The uncertainties are considered to be time-varying and bounded, but the bounds are unknown. We first established a dynamic model of the uncertain Cubli system, subject to the servo constraints. Next, we present the robust control with a leakage-type adaptive law. We used the Lyapunov theory to verify the stability of the control. Finally, the effectiveness of the control was verified through numerical simulation in MATLAB™.