Control methods based on regressor matrix and vector of uncertain variables, are the common approaches in control of nonlinear systems that are successfully extended to mobile robot control applications. To establish the controller in regressor based approaches, rewriting the process model in the parameterized form of regressor with uncertainties is essential. Evidently, this main drawback became a motivation for development of the regressor free control strategies. Controller design principle of the regressor free approaches are based on good estimation of the unknown dynamics by function approximation techniques (FAT). In this study, the systematic trajectory-tracking dynamic control design of nonholonomic mobile robot using (FAT) approach is illustrated. The robot dynamics is estimated using Fourier series approximation using variety of orthogonal basis functions such as Bessel, Laguerre, Chebyshev, and Legendre orthogonal basis functions. The function approximated dynamic of the system compliance with stability requirements is directly used in trajectory tracking control design of nonholonomic mobile robot. The results of the proposed method is compared with the inverse dynamic control method, two main regressor based adaptive inverse dynamics, and passivity based adaptive control approaches. The impressive quality of the performance of FAT based control algorithm is presented.