This paper presents a robust impedance controller for robot manipulators using function approximation techniques (FATs). Recently, some FAT-based robust impedance control approaches have been presented using Fourier series expansion or Legendre polynomials for uncertainty estimation. However, the dimensions of regressor matrices in these approaches are relatively large. This problem becomes hypersensitive especially for higher degree of freedom robot manipulators. In this paper, a simpler and less computational FAT-based robust controller is presented without considering discontinuous nonlinearities. It is assumed that the lumped uncertainty can be modelled by a linear differential equation with unknown coefficients. Then, using the Stone-Weierstrass theorem, it is verified that these differential equations are universal approximators. The advantage of the proposed controller in comparison with previous related works is reducing the dimensions of regressor matrices. Simulation results on a Puma560 robot manipulator indicate the efficiency of the proposed method.