This paper focuses on the application of quadratic optimization for the approximation of uncertain nonlinear robotic function. This function will be used to perform the task of motion control to feedback control of robotic systems. To achieve this task, we are trying, through the study and simulation four approximation approaches: Power Series Polynomial Approximation (PSPA), Orthogonal Neural Network Approximation (ONNA), Chebyshev Polynomials and Series Approximation (CP& SA) and Least Squares Chebyshev polynomial approximation (LSCPA). In each case mentioned above, we use the orthogonal polynomial approximation in higher dimension spaces, which enable us to modify classical differential equation solvers to perform high precision, nonlinear term in model robotic. We unify and extend classical results from function approximation theory and consider their utility in robotics. Then, we could use an efficient algorithms for solving any robust control problems of manipulator robot. Simulation results from a two-link robot manipulator show the satisfactory performance of the approach of approximation the nonlinear term in model robotic.