## Methods
### Design of Unmanned Agricultural Machine Operation under Improved Fuzzy Adaptive Algorithm
#### 3.1.1 Kinematic Model and Improved Adaptive Algorithm Design
So, this study considers the fuzzy adaptive scheduling (priority-driven scheduling, PD) control algorithm to achieve the adjustment of the deviation results, which ensures the stability and rapidity of the path tracking algorithm. PD (proportional-differential) control and PID (proportional-integral-differential) control are two common feedback control algorithms. The difference lies in whether they contain an integral term (I). The integral term in the PID controller can respond by integral deviation, which is affected by cumulative error interference and affects the efficiency of algorithm processing. There is no obvious steady-state error in the path tracking control of actual agricultural machinery, and the reduction in integral terms is not necessary. Its reduction can also simplify control algorithms and reduce computational burden. And in the research using PD control, nonlinear control algorithms are also introduced to eliminate errors, which can ensure algorithm accuracy. By using simulation models and setting the initial heading angle deviation and lateral deviation, agricultural machinery movement speed, and vehicle wheelbase, it was found that when the differential adjustment coefficient is small, the online speed of agricultural machinery is faster, but the stability is poor. According to PD control theory, increasing the proportional adjustment coefficient can make the system response faster, while increasing the differential adjustment coefficient can reduce system overshoot and enhance stability. Therefore, research is conducted on setting fuzzy rules to ensure that the control algorithm has good path tracking accuracy. If the lateral deviation is \"small\" and the heading angle deviation is \"small\", then increase the proportional gain and differential gain. If the lateral deviation is \"medium\" and the heading angle deviation is \"medium\", then slightly increase the proportional gain and differential gain. If the lateral deviation is \"large\" or the heading angle deviation is \"large\", then decrease the proportional gain and differential gain. The adjustment of the proportional gain and differential gain is to improve the dynamic response of the system and reduce overshoot. The specific fuzzy control rules are shown in Table 2.  
The domain for setting the control parameters is [1, 3.5], the quantisation factor is 1, and the quantisation level can be divided into {1,1.7, 2.3, 2.9, 3.5}. The domain for lateral deviation and heading angle deviation is [\(-0.5\) m, \(0.5\) m] and [\(-30^{\circ}\), \(30~{}^{\circ}\)], and the quantisation level is divided into {\(-5\), \(-2.5\), \(0.5\)}. The membership functions for the control parameters, lateral deviation, and heading angle deviation are all Gaussian functions, and the membership functions for each variable are shown in Figure 3. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Control Parameters**} & \multicolumn{5}{c}{** Lateral Deviation**} \\ \cline{3-6}  & & \(-\)**5** & \(-\)**2.5** & **0** & **2.5** & **5** \\ \hline \multirow{6}{*}{Heading angle deviation/\({}^{\circ}\)} & \(-\)5 & 1 & 1.7 & 2.3 & 1.7 & 1 \\ \cline{2-6}  & \(-\)2.5 & 1.7 & 2.3 & 2.9 & 2.3 & 1.7 \\ \cline{1-1} \cline{2-6}  & 0 & 2.3 & 2.9 & 3.5 & 2.9 & 2.3 \\ \cline{1-1} \cline{2-6}  & 2.5 & 1.7 & 2.3 & 2.9 & 2.3 & 1.7 \\ \cline{1-1} \cline{2-6}  & 5 & 1 & 1.7 & 2.3 & 1.7 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Fuzzy control rules. This study uses lateral deviation and heading angle deviation as the inputs for fuzzy controllers. The parameters of the PD controller are taken as the output of the fuzzy controller and input the control rules in the fuzzy logic design tool. The sensors collect the information about the current state and operating environment of the agricultural machinery, and the fuzzy controller receives input signals and processes them using fuzzy logic. The signals are fuzzified based on a preset fuzzy set and rule library.