This paper, proposes a methodology to implement a suitable nonsingular terminal sliding mode controller associated with the output feedback control to achieve a successful trajectory tracking of a non-holonomic wheeled mobile robot in presence of longitudinal and lateral slip accompanied. This implementation offers a relatively faster and high precision tracking performance. We investigate this approach and demonstrate its feasibility for such situations where robustness against perturbation and measurement errors are required. In this study, tyre-forces are considered as perturbation. These forces appear because of wheel slip of the wheeled mobile robot moving at high speed or on a slippery surface. The need to compensate these forces are achieved through a design of an intelligent estimation paradigm. The estimator is realized by a fuzzy logic model that requires slip angle and slip ratio as inputs. The weight of the robot mechanical structure is an important parameter in this design. In fact, it is used to adjust the gain of the output, resulting in a fuzzy estimator that synthesizes the magic formula for a large model of tyres. Simulation results are reported and discussed.