Nonsingular BLF-Based Simultaneous Tracking and Balancing Control of Uncertain Ball-Balancing Robots With Moving Obstacles: A Virtual-Angle Approach

Abstract

This paper proposes a nonsingular virtual-angle control method for uncertain underactuated ball-balancing robots (BBRs) subject to trajectory tracking, posture stabilization, and obstacle avoidance requirements. Because tracking and balancing are strongly coupled in BBR systems, conventional hierarchical sliding mode control may suffer from local-minimum issues. In addition, existing virtual-angle-based methods can become unreliable when the internally generated posture demand grows excessively during aggressive transients. To overcome these limitations, a normalized nonsingular barrier Lyapunov function (BLF) is incorporated into the reference-generation process so that the tracking-side motion is constrained in advance and the virtual angle remains well posed. A trajectory-modulation mechanism is further developed to coordinate tracking recovery and obstacle avoidance, while radial basis function neural networks are employed to compensate for uncertain nonlinear dynamics. It is shown that the virtual angle remains bounded prior to the posture-controller design, and Lyapunov-based analysis guarantees uniform ultimate boundedness of all closed-loop signals together with prescribed state constraints and obstacle avoidance. Comparative simulations show bounded transient behavior and satisfaction of the prescribed constraints under the tested initial offsets and uncertainty conditions.