## 3 Results and Discussion
### Whole-Field Path-Tracking Test  
As shown in Figure 14, the performance of the ANS was further tested for whole-field path tracking, where the turning radius of the tractor was 6 m and both the FSM and SM were tested. The length and width of the test field were 40 m and 35 m, and the whole-field path included autonomous turning paths in the outer circle and manual turning paths in the inner loop. The travel speed for the straight path segments was controlled at 1 m/s, and, for the curved segments, it was controlled at 0.5 m/s. The operation width was set at 4 m.  
The whole-field path-tracking results of the SM and FSM are shown in Figures 15 and 16. Because there were multiple obstacles in the field, only part of the whole-field path tracking was performed, but straight paths and curved paths were included. It can be seen in the enlarged images in Figure 15 that the FSM not only performed better in the straight  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Average Speed** & \multirow{2}{*}{**Algorithm**} & \multicolumn{2}{c}{**Guiding**} & \multirow{2}{*}{**MTE (cm)**} & \multirow{2}{*}{**ATE (cm)**} & \multirow{2}{*}{**STDE (cm)**} \\
**(m/s)** & & & & & \\ \hline \multirow{2}{*}{0.5} & SM & 5.3 & 10.0 & 4.1 & 3.2 \\  & FSM & 2.8 & 8.0 & 3.3 & 3.1 \\ \hline \multirow{2}{*}{1} & SM & 6.9 & 12.0 & 5.8 & 4.0 \\  & FSM & 4.4 & 10.0 & 5.2 & 3.4 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Results of path tracking at different speeds.  
Figure 12: Results of path tracking at a speed of 0.5 m/s. (**a**) Trajectory tracking; (**b**) lateral error.  
Figure 13: Results of path tracking at a speed of 1 m/s. (**a**) Trajectory tracking; (**b**) lateral error.  
path segments but also reduced the lateral tracking error in the curved segments, which coincides with the tracking error shown in Figure 16. In Figure 16, both the tracking error of straight-line (SL) and curved paths are shown. An enlarged image of the straight-line segment is shown in the second row, where the FSM significantly outperformed the SM. More specific results are listed in Table 8. The MTE of the FSM for whole-field path tracking was 27 cm, and for the SM, it was 34 cm. The maximum error appeared in the curved segments, which did not affect the working quality of the tractor inside the field. Compared to the SM, the ATE for the FSM was reduced from 9.6 cm to 8.1 cm with an STDE of 9.4 cm, indicating that the designed ANS is suitable for whole-field path tracking.  
In the implementation of the ANS, only the roll and heading are involved in position offset correction, which is often not enough for complicated field soils, e.g., for the autonomous turning stages, the pitch error should also be imported. It is noted in Figure 16  
Figure 14: Whole-field path-tracking test site.  
Figure 15: Results of the trajectory for whole-field path tracking.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Algorithm** & **MTE (cm)** & **ATE (cm)** & **STDE (cm)** \\ \hline SM & 34.0 & 9.6 & 11.3 \\ FSM & 27.0 & 8.1 & 9.4 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Whole-field path-tracking results.  
that the FSM achieved a more stable transition period than the SM in the curved-straight-line switching stage, which coincides with the results shown in Figure 13. However, as the FSM could not reduce the guiding trajectory distance efficiently, there was still an obvious deviation error in cases where the tractor started straight path tracking in the path-switching stage, which should be further improved by using other optimization algorithms.