In this paper, a neural-network-based control method to achieve trajectory tracking and balancing of a ball-balancing robot with uncertainty is presented. Because the ball-balancing robot is an underactuated system and has nonlinear couplings in the dynamic model, it is challenging to design a controller for trajectory tracking and balancing. Thus, various approaches have been proposed to solve these problems. However, there are still problems such as the complex control system and instability. Therefore, the objective of this paper was to propose a solution to these problems. To this end, we developed a virtual angle-based control scheme. Because the virtual angle was used as the reference angle to achieve trajectory tracking while keeping the balance of the ball-balancing robot, we could solve the underactuation problem using a single-loop controller. The radial basis function networks (RBFNs) were employed to compensate uncertainties, and the controller was designed using the dynamic surface control (DSC) method. From the Lyapunov stability theory, it was proven that all errors of the closed-loop control system were uniformly ultimately bounded. Therefore, the control system structure was simple and ensured stability in achieving simultaneous trajectory tracking and balancing of the ball-balancing robot with uncertainty. Finally, the simulation results are given to verify the performance of the proposed controller through comparison results. As a result, the proposed method showed a 19.2% improved tracking error rate compared to the existing method.

This article proposes a virtual angle-based adaptive control method for trajectory tracking and balancing of ball-balancing robots without velocity measurements.The trajectory tracking and balancing control of ball-balancing robots is challenging due to underactuation and uncertain nonlinearities. The hierarchical control strategy, which designs the control system using a linear combination of trajectory tracking and balancing errors, can be a solution. However, it has a local minimum problem where the convergence of tracking and balancing errors is not guaranteed even though the linear combination error is zero. Therefore, a virtual angle-based control method is presented, which can solve the underactuation problem without the local minimum issue. In addition, a neural network-based observer is developed to estimate the velocity information of ball-balancing robots with uncertainties, and the input saturation problem is considered. It is proven that all tracking and balancing errors are bounded and can be made arbitrarily small in the Lyapunov sense. Finally, simulation results are provided to verify the effectiveness of the proposed control system.

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