Robust Control for Trajectory Tracking and Balancing of a Ballbot

This article presents a robust control method for trajectory tracking and balancing of a ballbot with uncertainty. Since the ballbot is an underactuated system, previous studies have designed controllers using a hierarchical strategy and/or multi-loop approach. However, multi-loop control systems require several controllers and the hierarchical strategy has a local minimum problem that does not guarantee the convergence of all errors globally. To overcome these drawbacks, we introduce a virtual angle and design a sliding mode controller with a single-loop control system. As a result, the proposed controller is simple and can achieve simultaneous tracking and balancing of the ballbot. From Lyapunov stability theory, it is proven that the tracking and balancing errors of the ballbot are uniformly ultimately bounded and can be made arbitrarily small. Finally, simulation results are presented to verify the proposed control system.