# The Full-Field Path Tracking of Agricultural Machinery Based on PSO-Enhanced Fuzzy Standley Model
## 4 Results and Discussion
### Mobile Vehicle Autonomous Navigation Test  
In order to verify the effectiveness of the proposed PSO-SM, a real-time autonomous navigation test is performed by employing a mobile vehicle, as shown in Figure 8. The dual-antenna RTK position system is applied to provide the position, velocity, heading  
Figure 7: Autonomous turning under different scenarios. (**a**) Autonomous turning under ideal scenario; (**b**) Autonomous turning under high-speed scenario; (**c**) Autonomous turning under steering actuator saturation scenario. and pitch information of the mobile vehicle. The base station receiver is OEM719 and the mobile station receiver is OEM718D (provided by NovAtel Inc., Calgary, AB, Canada), where the positioning accuracy is 1 cm + 1 ppm and heading accuracy is 0.08\({}^{\circ}\) with a 2 m antenna baseline. The update frequency of the dual-antenna RTK is 5 Hz. The motor driver RMDS405 supports 30 A current (provided by Shenzhen RoboModule Technology Co. Ltd., Shenzhen, China), and the encoder is Omron E6B2 with a resolution up to 3600 P/R. The navigation decision system NavLight (with Version 4.07) is built by the intelligent agricultural machinery team of Jiangsu University (Zhenjiang, China), which includes a full-field path plan and navigation signal processing and the cross-platform navigation software based on Qt works well by using multi-thread coding technology. First, predefined path information is generated utilizing the position information of the farmland. Second, the real-time heading and position information is sent to navigation PC and then lateral deviation and heading deviation are calculated and sent to the embedded controller. Finally, the controller calculates the desired steering angle based on the navigation deviation and sends the control information to the motor driver via the CAN bus at a frequency of 5 Hz. The motor driver converts the control command into voltage and receives feedback from the encoder to form a closed-loop control system, which can control the motor at 100 Hz. In order to verify the adaptability of PSO-FSM to different path curvatures and speeds of agricultural machinery, the full-field working path for the combine harvester is designed. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Velocity (m/s)** & **Steering Angle Scaling** & **Algorithm** & **MAE (cm)** & **RMSE (cm)** \\ \hline
1 & 1 & SM & 1.1 & 36.1 \\
1 & 1 & FSM & 0.4 & 13.6 \\
1 & 1 & PSO-FSM & 0.3 & 12.4 \\
3 & 1 & SM & 9.2 & 93.7 \\
3 & 1 & FSM & 1.8 & 28.7 \\
3 & 1 & PSO-FSM & 0.9 & 15.6 \\
1 & 0–1 & SM & 20.9 & 48.1 \\
1 & 0–1 & FSM & 5.4 & 16.2 \\
1 & 0–1 & PSO-FSM & 0.3 & 12.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Path tracking result under different scenarios. Figure 8: Setup for mobile vehicle path tracking test. As it is shown in Figure 9, a hybrid path is designed for the combine harvester of large operating width, where the outer circle is composed of autonomous turning path and the arrows indicate the driving direction. If half of the remaining field width is less than the turning radius of the combine harvester, the turning at the field head is carried out by manual driving, which is more efficient than autonomous turning with back-up control. The combine harvester performs harvesting operations in sequence. When the remaining field width is smaller than the size required for the harvester to carry out autonomous turning, the navigation PC sends a signal to the controller before the end of last straight line for autonomous turning, e.g., straight line 4 in Figure 9, and then automatically switches to the manual-assisted driving mode. The full-field path tracking of the combine harvester can be divided into the guiding stage, straight line and curve path tracking stage. The lateral tracking error of SM for the straight line is small, and the fixed output gain can achieve acceptable result, thus the guiding and curve path tracking stages are our main focuses in this work.