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A model for the dynamic process of wheeled tractor driving, which combined a dynamic model containing road slope disturbance and a tracking error model, to address the issue of reduced accuracy of path tracking control algorithms caused by lateral sloping farmland terrain in some regions was proposed. Based on this model, a linear model predictive control method was used to obtain the control law. As the predictive model included the influence of slope, which enabled feedback correction to be compensated in advance, effectively improving the path tracking performance of agricultural machinery on sloping land. Considering the different requirements for error and stability of agricultural machinery in different driving stages, an adaptive model prediction method was proposed, which allowed the Q and R values to vary dynamically to meet different needs. Here, the variation referred to the relative size of the two, rather than the absolute value. Experiments were conducted on the selection of prediction intervals and control intervals. Then, a comparative experiment was conducted on the model predictive control based on a simple kinematic model with or without adaptive for Q and R. Finally, comparative experiments were conducted with the proposed method and the model predictive control method based on simple kinematics on a fixed slope angle transverse slope road surface and a continuously changing slope angle transverse slope road surface, respectively. Experiments showed that adaptive control can significantly improve control effectiveness, the path tracking performance of the method proposed was significantly better than that based on simple kinematic models on lateral sloping roads, and the stability level was also significantly improved in steady-state.