This paper presents an adaptive impedance control scheme for an $n$-link constrained rigid robot manipulator without using the regressor. In addition, inversion of the estimated inertia matrix is also avoided and the new design is free from end-point acceleration measurements. The dynamics of the robot manipulator is assumed that all of the matrices in robot model are unavailable. Since these matrices are time-varying and their variation bounds are not given, traditional adaptive or robust designs do not apply. The function approximation technique is used here to represent uncertainties in some finite linear combinations of the orthogonal basis. The dynamics of the output tracking can thus be proved to be a stable first order filter driven by function approximation errors. Using the Lyapunov stability theory, a set of update laws is derived to give closed loop stability with proper tracking performance. A 2 DOF planar robot with environment constraint is used in the computer simulations to test the efficacy of the proposed scheme.