# The Full-Field Path Tracking of Agricultural Machinery Based on PSO-Enhanced Fuzzy Standley Model
## 4 Results and Discussion
### Mobile Vehicle Autonomous Navigation Test
The initial parameter setting of SM and PSO-FSM is the same as the numerical simulation to make a fair comparison. The average speeds of the mobile vehicle for the straight line and autonomous turning stages are 2.5 m/s and 0.8 m/s, respectively, i.e., the vehicle reduces its speed automatically before starting the curve path tracking. The path tracking trajectories of different algorithms for one U turning are shown in Figure 10, where both the guiding trajectory and curve path tracking result are included. It is notable in Figure 10a that PSO-FSM reduces the guiding distance of the mobile vehicle when the initial lateral deviation is set as 4 m, where the guiding distance is less than 5 m. In Figure 10b, because of the time-varying tracking error and steering actuator saturation, the performance of SM is degraded a lot compared with the straight line tracking. It is important to note that PSO-FSM outperforms SM which coincides with the numerical simulation, i.e., SM cannot achieve stability and precision path tracking by use fixed gain coefficient for time-varying curvature and disturbance. PSO and fuzzy inference improve SM significantly by employing a cascaded optimization structure to change the gain coefficient adaptively. The parameter variation in PSO-FSM is shown in Figure 11, where Figure 11a is the gain coefficient \(k\) of the path tracking test based on PSO-FSM. It is notable that \(k\) is updated adaptively according to the deviation change, and its value is reduced quickly when the path tracking of the curve segment is finished. Figure 11b is the expected front wheel steering angle calculated by the embedded controller. It is notable that when the curvature is changed, the expected steering angle changed accordingly, which presents different results with respect to the output gain coefficient variation. Figure 9: Full-field path planning schematic of the combine harvester. The tracking error of the different algorithms is shown in Figure 12, where the lateral errors of the straight line and curve segment are given. Notice that PSO-FSM reduces the guiding distance of the autonomous vehicle in Figure 12a, whereas once the path tracking is stable, i.e., after the vehicle runs after about 5 s, there is no obvious difference between SM and PSO-FSM. Both the algorithms achieve a maximum lateral tracking error less than 3 cm with a standard deviation less than 1 cm. However, the steady-state error of SM in the curve segment is improved significantly by PSO-FSM, where the maximum lateral error is reduced from 32 cm to 3 cm. In order to verify the full-field unmanned driving ability of the proposed algorithm, the full-field path tracking result of the mobile vehicle is shown in Figure 13, and the detail tracking errors are listed in Table 3. As we can see, PSO-FSM not only improves the guiding performance of the autonomous vehicle but also reduces the tracking error significantly. The maximum tracking error of PSO-FSM is less than 3 cm in the full-field path tracking test, which results from the fact that the uncertain disturbances of the mobile vehicle path tracking on a dry pavement is well handled by the cascaded path tracking algorithm. When analyzing the experiment data, we notice that there is an obvious steady-state error in the straight line segment, which may result from the mechanical clearance of the steering control system and misalignment error between GNSS baseline and the forward direction of the mobile vehicle. In the application of large agricultural machinery, the error  
Figure 11: Parameters of the path tracking based on PSO-FSM. (**a**) Gain coefficient of the path tracking; (**b**) Expected steering angle of the path tracking. Figure 10: Path tracking result under different scenarios. (**a**) Guiding trajectory with large initial lateral error; (**b**) Curve path tracking of autonomous turning. coming from the mechanical clearance of the steering control system is negligible and the misalignment error can be further compensated by field calibration [34].