This article discusses the design of generalised proportional integral observers for the tracking control of robot manipulators. The unknown, possibly state-dependent, additive nonlinearity influencing the input-output description, in terms of the tracking error dynamics is modelled for observer construction purposes, as an absolutely bounded, additive, unknown time-varying perturbation input signal. A disadvantage of the approach lies in the fact that the system inertia matrix is usually required for implementation. In this work, it is shown how the approach can be modified to avoid the use of the inertia matrix when it is unknown. A set of experiments with three different test beds is carried out to show the good performance of the proposed algorithm.