A major problem in the design of control laws dedicated to mobile robots appears when the classical hypothesis of rolling without sliding wheels is violated. It is generally the case for off-road vehicles as adherence conditions are often not satisfactory and sliding can then cease to be negligible. Consequently theoretical performance is impaired and the vehicle is no longer accurately controlled. It is particularly harmful with respect to path tracking tasks, where a loss of accuracy in rough terrain can generate a hazardous situation. Previous work based on the assumption of rolling without sliding has shown very satisfactory results with respect to that task when sliding is not preponderant. It has also made it possible to pinpoint and study the effects of sliding when it appears to be non-negligible. To preserve path tracking accuracy with respect to this phenomenon, a new control law based on an extended kinematic model (updated on-line via an adaptive method) is proposed and discussed. Such control is very efficient when adherence conditions are constant, but overshoots can appear when an abrupt variation is recorded (which is especially the case at the beginning/end of curves due to low level delays and inertial effects). A Model Predictive Control approach is then added to limit such transient phases in cases where a curved path is followed. The paper is organized as follows: the extended kinematic model is presented as well as the observation of unmeasured parameters required to feed it. A non-linear control law can then be designed and the results obtained are discussed. Finally, the Model Predictive Control approach is integrated and the overall control scheme is presented. The capabilities of the approach described in this paper are then discussed through full scale experiments.