Path Tracking Control Algorithm of Tractor-Implement

Abstract

[Objective]The usual agricultural machinery navigation focuses on the tracking accuracy of the tractor, while the tracking effect of the trailed implement in the trailed agricultural vehicle is the core of the work quality. The connection mode of the tractor and the implement is non-rigid, and the implement can rotate around the hinge joint. In path tracking, this non-rigid structure, leads to the phenomenon of non-overlapping trajectories of the tractor and the implement, reduce the path tracking accuracy. In addition, problems such as large hysteresis and poor anti-interference ability are also very obvious. In order to solve the above problems, a tractor-implement path tracking control method based on variable structure sliding mode control was proposed, taking the tractor front wheel angle as the control variable and the trailed implement as the control target.[Methods]Firstly, the linear deviation model was established. Based on the structural relationship between the tractor and the trailed agricultural implements, the overall kinematics model of the vehicle was established by considering the four degrees of freedom of the vehicle: transverse, longitudinal, heading and articulation angle, ignoring the lateral force of the vehicle and the slip in the forward process. The geometric relationship between the vehicle and the reference path was integrated to establish the linear deviation model of vehicle-road based on the vehicle kinematic model and an approximate linearization method. Then, the control algorithm was designed. The switching function was designed considering three evaluation indexes: lateral deviation, course deviation and hinged angle deviation. The exponential reaching law was used as the reaching mode, the saturation function was used instead of the sign function to reduce the control variable jitter, and the convergence of the control law was verified by combining the Lyapunov function. The system was three-dimensional, in order to improve the dynamic response and steady-state characteristics of the system, the two conjugate dominant poles of the system were assigned within the required range, and the third point was kept away from the two dominant poles to reduce the interference on the system performance. The coefficient matrix of the switching function was solved based on the Ackermann formula, then the calculation formula of the tractor front wheel angle was obtained, and the whole control algorithm was designed. Finally, the path tracking control simulation experiment was carried out. The sliding mode controller was built in the MATLAB/Simulink environment, the controller was composed of the deviation calculation module and the control output calculation module. The tractor-implement model in Carsim software was selected with the front car as a tractor and the rear car as the single-axle implement, and tracking control simulation tests of different reference paths were conducted in the MATLAB/Carsim co-simulation environment.[Results and Discussions]Based on the co-simulation environment, the tracking simulation experiments of three reference paths were carried out. When tracking the double lane change path, the lateral deviation and heading deviation of the agricultural implement converged to 0 m and 0° after 8 s. When the reference heading changed, the lateral deviation and heading deviation were less than 0.1 m and less than 7°. When tracking the circular reference path, the lateral deviation of agricultural machinery tended to be stable after 7 s and was always less than 0.03 m, and the heading deviation of agricultural machinery tended to be stable after 7 s and remained at 0°. The simulation results of the double lane change path and the circular path showed that the controller could maintain good performance when tracking the constant curvature reference path. When tracking the reference path of the S-shaped curve, the tracking performance of the agricultural machinery on the section with constant curvature was the same as the previous two road conditions, and the maximum lateral deviation of the agricultural machinery at the curvature change was less than 0.05 m, the controller still maintained good tracking performance when tracking the variable curvature path.[Conclusions]The sliding mode variable structure controller designed in this study can effectively track the linear and circular reference paths, and still maintain a good tracking effect when tracking the variable curvature paths. Agricultural machinery can be on-line in a short time, which meets the requirements of speediness. In the tracking simulation test, the angle of the tractor front wheel and the articulated angle between the tractor and agricultural implement are kept in a small range, which meets the needs of actual production and reduces the possibility of safety accidents. In summary, the agricultural implement can effectively track the reference path and meet the requirements of precision, rapidity and safety. The model and method proposed in this study provide a reference for the automatic navigation of tractive agricultural implement. In future research, special attention will be paid to the tracking control effect of the control algorithm in the actual field operation and under the condition of large speed changes.

Keywords

• trailed implement
• kinematic model
• sliding mode variable structure control
• path tracking
• simulation test