An Adaptive Model Uncertainty Estimator Using Delayed State-Based Model-Free Control and Its Application to Robot Manipulators

In this article, we propose an innovative model-free control (MFC) algorithm using an adaptive model uncertainty estimator (AMUE) that provides stable torque input while allowing more precise control, even in the presence of instantaneous disturbances, such as friction, payload, or trajectory changes. Unlike traditional time-delay estimation (TDE)-based controllers that directly use one-sample delayed signals to estimate unmodeled dynamics and uncertainties, the proposed algorithm achieves better tracking performance by considering not only the one-sample delayed signal but also its gradient with an adaptive gain. Furthermore, the proposed adaptive estimator works well independently of conventional TDE-based controllers, providing a wide range of control gains. This implies that the proposed approach provides the opportunity to strategically improve TDE-based controllers, which have performance limitations caused by conventional TDE technique errors. The proposed algorithm can be easily extended to different TDE-based controllers. Finally, the stability of the AMUE-MFC is guaranteed through the Lyapunov stability theory, and its performance is demonstrated via simulations and experiments with robotic manipulators.