Stabilization of a vision-based ball-on-sphere system

This paper presents the design, implementation, and validation of the stabilization of a control laboratory experiment, called the ball-on-sphere system. This system consists of a sphere, two motors, and two friction wheels. On the top of the sphere, a small ball is balanced by rolling the sphere along each of two horizontal axes through friction wheels driven by motors. Control of this system is a challenging task because of inherent nonlinearity, instability, and underactuation. By retaining the predominant nonlinear terms and neglecting the high-order coupling terms, the system model of the ball-on-sphere system is simplified to two decoupled ball-and-wheel systems. Sliding mode control is then used to design the stabilizing controller for the simplified model. In addition, a linear-quadratic regulator controller is also designed for performance comparison. In the implementation of this control laboratory experiment, the position of the ball is measured with a machine vision system and the designed control schemes are realized through a digital signal processor. The effectiveness of the designed control schemes is verified through experimental studies. The experimental results show that the designed control schemes and machine vision system are able to stabilize the system in real-time.