Abstract:

【Objective】 Conventional steering systems for autonomous tractors often suffer from insufficient precision and robustness, making it difficult to meet the demands of high-accuracy trajectory tracking. Although single-motor steer-by-wire (SBW) systems proposed in previous studies can improve tracking precision, they are limited by restricted output torque and poor fault tolerance, especially under complex conditions such as low-speed and heavy-load operations. To address these issues, the aim is to develop a high-performance trajectory tracking control method based on a dual-motor SBW system, thereby improving tracking accuracy, robustness, and operational safety across a variety of working conditions. 【Methods】 A hierarchical control architecture was constructed in this study. At the upper level, a trajectory tracking controller was designed. Based on a two-wheel bicycle dynamic model of the tractor, a linear quadratic regulator (LQR) controller was developed to solve the optimal control problem and compute the desired front-wheel steering angle for trajectory tracking. At the lower level, a steering execution controller was developed for the dual-motor SBW system. First, a mathematical model incorporating both electrical and mechanical components of the system was established. To address nonlinearities and uncertainties, a sliding mode controller (SMC) was designed for each motor to achieve robust control. To mitigate the inherent chattering issue of SMC, a disturbance observer (DOB) was incorporated. The DOB continuously estimated the total disturbance in real time, including both external interferences and internal parameter variations, and provided feed-forward compensation. This compensation enabled a reduction in the switching gain of the SMC, thereby effectively suppressing chattering while maintaining robust performance. For dual-motor coordination, an independent control strategy was adopted, leveraging the identical parameters of both motors. Under this scheme, the two motors received the same steering angle command and operated in parallel, maintaining structural simplicity while enhancing system fault tolerance. The overall control strategy was structured as a hierarchical system, comprising an upper-level LQR trajectory tracking module and a lower-level steering execution module based on SMC+DOB. 【Results and Discussion】 To validate the effectiveness of the proposed method, both simulations and field experiments were conducted. Simulations were performed on a Matlab–Carsim co-simulation platform, specifically evaluating steering angle tracking performance and the disturbance rejection capability of the DOB. The results showed that, compared to the SMC controller without DOB, the SMC+DOB controller reduced the front-wheel steering angle tracking error by 13.12% while significantly suppressing chattering. Field experiments were carried out on a T954 tractor platform to evaluate the control strategy under realistic operating conditions. A representative working path, consisting of both straight and curved segments, was used, and tests were performed at two speeds: low speed (10 km/h) and high speed (30 km/h). To benchmark performance, three control strategies were compared: LQR+SMC, MPC+SMC+DOB, and the proposed LQR+SMC+DOB, enabling a comprehensive assessment of tracking accuracy, robustness, and real-time control effectiveness. The field experimental results show that: 1) All SBW-based methods significantly outperformed traditional steering in terms of lateral tracking error and heading error. 2) Under low-speed conditions, the proposed LQR+SMC+DOB method reduced the average lateral tracking error, heading error, sideslip angle, and front-wheel steering angle error by 19.9%, 40.2%, 6.5%, and 14.3%, respectively, compared to LQR+SMC. Under high-speed conditions, the corresponding reductions were 23.7%, 52.2%, 4.5%, and 27.3%. 3) Compared with MPC+SMC+DOB, the proposed LQR+SMC+DOB achieved similar trajectory tracking performance while significantly reducing the computation time per iteration. The above experimental results indicate that the adopted dual-motor SBW system effectively enhanced the steering output torque and system fault tolerance, thereby improving trajectory tracking accuracy and thus providing a hardware foundation for resolving the power and safety challenges in tractor heavy-load operations, and the designed SMC+DOB controller combined strong robustness with smooth control action, effectively suppressing external disturbances and markedly reducing chattering, thereby improving the accuracy and stability of steering execution. 【Conclusion】 This research successfully proposed and validated a high-precision trajectory tracking control strategy for autonomous tractors. By integrating an upper-level LQR trajectory tracking controller with a lower-level dual-motor SMC+DOB steering controller, a robust and efficient hierarchical control framework was established. This control strategy consistently exhibited excellent trajectory tracking performance and real-time capability across different speeds, offering a reliable technological solution for high-performance operations of autonomous tractors. In comparison with the MPC control strategy, the control strategy proposed in the study demonstrated exceptionally high computational efficiency, rendering it highly suitable for real-time control applications.

Key words: autonomous tractor, trajectory tracking, steer by wire, LQR, SMC, disturbance observer