Robust adaptive impedance control of robot manipulators using Szász-Mirakyan operator as universal approximator

In the present work, impedance control of robot manipulators is enhanced. The controller is designed by using Szász-Mirakyan operator as Universal approximator. Although the Szász-Mirakyan operator has been extensively used for dealing with approximation of nonlinear functions, the main novelty of this paper is presenting a completely different application of Szász-Mirakyan operator. Since in robust or adaptive control, the nonlinear function which should be approximated is unknown. In fact, the Lyapunov theorem must be used to tune its adjustable parameters. In accordance with the universal approximation theorem, Szász-Mirakyan operator which is an extended version of the Bernstein polynomial is able to approximate uncertainties including un-modeled dynamics and external disturbances. This fact is completely discussed in this paper. It is shown that, using Szász-Mirakyan operator as basis functions and tuning the polynomial coefficients by the adaptive laws calculated in the stability analysis, uniformly ultimately bounded stability can be assured. The transient performance of the controller has been also analyzed. Numerical simulations on an electrically driven manipulator are provided. Simulation results verify that the role of Szász-Mirakyan operator in uncertainty compensation and enhancing the tracking error is undeniable.