## 4 Results and Discussion
of the agricultural machinery is set to 1.06 m. Figure 8 shows the results of the driving path tracking. The results in Figure 8 show that the lateral deviation curves of the PD control algorithm under different travelling distances vary with large ups and downs, and their maximum and minimum values reach 0.046 and \(-\)0.032, respectively, with obvious fluctuations. The fuzzy adaptive PD algorithm, on the other hand, has a smaller deviation value in path tracking, and shows better stability overall, with its average absolute error reaching 0.0425. Considering the absolute value of deviation of the multi-deviation feedback control algorithm, the absolute value of deviation maxes out at 0.0243 m, and the average absolute error turns out to be less than 0.005 m, which is of high tracking accuracy. The result in Figure 8 indicates that traditional PD control algorithms use proportional and differential terms to respond to errors, making it difficult to handle the dynamic characteristics of nonlinear systems of agricultural machinery in operating environments. When there are disturbances (such as terrain undulations, soft soil, wind interference, etc. ), it may lead to a decrease in tracking performance. The performance of the PD algorithm highly depends on the selection of control parameters. If the parameters are not properly adjusted to adapt to the specific conditions of agricultural machinery operation, it can also lead to poor control effectiveness. The control algorithm proposed in this study is a combination algorithm that can effectively handle uncertainty and adapt to complex environments. Then, the performance of the control algorithm proposed in this study is further compared with PD control [32] and adaptive control [33], and the results are shown in Figure 9.  
Figure 8: Driving path tracking results of different algorithms. In the results of Figure 9, under the concrete pavement (Figure 9a), the fuzzy adaptive algorithm proposed in this study has a faster response speed compared to the PD algorithm with fixed parameters. When the travelling distance is less than 10 m, the PD algorithm and the path algorithm have higher overshooting and their degree of undulation is higher. They then tend to stabilise with the increase in the travelling distance, but their average absolute deviation and maximum absolute deviation are significantly larger than that of the research-proposed algorithm. Under the paddy field environment (Figure 9b), when the system reaches the steady state, the maximum absolute deviation of the fuzzy adaptive control algorithm among them reaches 0.2016, and the corresponding differences with the PD parameter and tracking control algorithm are all above 0.13. The changing trend of this curve is basically floating at \(\pm\)0.15 m deviation, and the result of the deviation between the maximum and the minimum is smaller than that of the other two algorithms. The average absolute deviation of the PD parameter and tracking control algorithms have mean absolute deviation results of 0.0715 and 0.0689, which are much larger than the algorithm proposed in this study (0.0216). The research-proposed algorithm has a smaller regulation coefficient, better overall response and adaptability, and higher robustness in complex operating environments. We compare the proposed control algorithm with traditional control algorithms, and the results are shown in Figure 10.  
The results in Figure 10 indicate that when the starting point of the controller is at the origin, the traditional PID control system exhibits significant lateral deviation, and there is a significant discrepancy between its path planning results and the reference path. The lateral deviation under the adaptive fuzzy control proposed in this study is smaller than the fixed-time domain result, and the error value between it and the reference path  
Figure 10: Path planning results of different control algorithms. Figure 9: Lateral deviation results in two testing scenarios. is smaller.