In this paper, the problem associated with accurate control of a two-wheel steering mobile robot following a path is addressed thanks to a backstepping control strategy. This approach involves an observer to estimate the grip conditions, based on previous work, and the proposed control algorithm for the front axle. Since the significant parameters of the grip conditions are available from the observer, namely the sideslip angles and the cornering stiffnesses, it is then suitable to include them into an algorithm to control mobile robots and obtain a more accurate path tracking. This is made possible by gathering into a single backstepping approach both kinematic and dynamic models. This new point of view permits to take account of both kinematic and dynamic behaviors and grip parameters in the control law. The proposed approach is experimentally evaluated at different speeds and compared with two other state-of-the-art path tracking algorithms and evaluated for several values of lateral deviations.