In automatic guidance of agriculture vehicles, lateral control is not the only requirement. Lots of research works have been focused on trajectory tracking control which can provide high longitudinal-lateral control accuracy. Satisfactory results have been reported as soon as vehicles move without sliding. But unfortunately pure rolling constraints are not always satisfied especially in agriculture applications where working conditions are rough and not expectable. In this paper the problem of trajectory tracking control of autonomous farm vehicles in presence of sliding is addressed. To take sliding effects into account, two variables which characterize sliding effects are introduced into the kinematic model based on geometric and velocity constrains in presence of sliding. With linearization approximation a refined kinematic model is obtained in which sliding appears as additive unknown parameters to the ideal kinematic model. By integrating parameter adaptation technique with backstepping method, a stepwise procedure is proposed to design a robust adaptive controller. It is theoretically proven that for the farm vehicles subjected to sliding, the longitudinal-lateral deviations can be stabilized near zero and the orientation errors converge into a neighborhood near the origin. To be more realistic for agriculture applications, an adaptive controller with projection mapping is also proposed. Simulation results show that the proposed (robust) adaptive controllers can guarantee high trajectory tracking accuracy regardless of sliding.