Virtual angle‐based adaptive control for trajectory tracking and balancing of ball‐balancing robots without velocity measurements

Abstract

SummaryThis 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.