Control design of mobile robots dedicated to path tracking tasks is generally based on the rolling without sliding assumption at the wheel/ground contact point. However, such an hypothesis is not relevant for off-road vehicle and the use of non sliding assumption in this case leads to important tracking errors. Moreover, the vehicles considered for offroad applications (such as agricultural tasks) have generally important mass and inertia and are equipped with low reactive actuators. As a result, delays are introduced into the control loop, which depreciate considerably the performances of autonomous path tracking, especially during a modification of path curvature. This paper proposes several developments, relying on adaptive and predictive observer-based control, dedicated to automatic guidance of off-road mobile robots. The relevancy of the proposed algorithm is investigated via full scale experiments, carried out with a farm tractor, as the considered application is agricultural work.