## Methods
### Design of Unmanned Agricultural Machine Operation under Improved Fuzzy Adaptive Algorithm
#### 3.1.1 Kinematic Model and Improved Adaptive Algorithm Design
After fuzzy reasoning, the generated fuzzy output is converted into an accurate control signal, and its output value is converted into a control command or control signal. The front wheel angle can be transformed into a mathematical expression under fuzzy control, see Equation (4). \[\delta=K_{p}d+K_{d}v\varphi \tag{4}\]  
In Equation (4), \(K_{d}\) denotes the differential adjustment coefficient of the PD control algorithm, and \(K_{p}\) is the proportional adjustment coefficient. The range of the front wheel angle of the agricultural crop machine is limited to plus or minus 90\({}^{\circ}\), and the output results are nonlinearly processed with an inverse tangent function to obtain the tracking algorithm under the controller, see Equation (5). \[\delta t=\arctan(K_{p}d+K_{d}\varphi\varphi) \tag{5}\]  
In Equation (5), \(\arctan\) is the arctangent function, and \(\delta t\) is the front wheel angle under control processing. Based on the above, the tracking model for the control simulation can be obtained, see Figure 4.  
Figure 3: Variable membership function. When the current and subsequent path tracking deviations of the crop machine are opposite, it will lead to positive and negative fluctuations in the lateral deviation results. In order to simplify the control algorithm process and improve the performance of the automatic driving of the farming machine, this study is based on the relationship between the two input deviations and proposes a nonlinear control algorithm combining the lateral deviation and heading angle deviation since the steering angle error is eliminated. Therefore, the desired front wheel steering angle control can be expressed as Equation (6). \[\delta^{\prime\prime}=\varphi+\arctan\frac{k^{\prime}d}{v} \tag{6}\]  
In Equation (6), \(k^{\prime}\) is an adjustable control parameter. The result of the lateral deviation of the tracking path of the agricultural machine is related to the amount of control of the turning angle. So, this study considers the reduction in the desired path deviation and the oscillatory situation during tracking by adjusting the turning angle of the vehicle, so the steering deviation of the agricultural machine is replaced by the deviation at the front wheels, and Equation (7) is obtained. \[d_{front}=d-L\sin\theta \tag{7}\]  
In Equation (7), \(d_{front}\) is the lateral deviation at the front wheel. And the partial integration link is introduced to reduce the Vitae error to obtain the corner equation under the deviation combination control, see Equation (8). \[\delta^{\prime\prime\prime}=\varphi+k_{1}\arctan\frac{k_{2}(d-L\sin\theta)}{v} +k_{i}I_{\text{int}} \tag{8}\]  
In Equation (8), \(k_{1}\) denotes the weight of the position deviation feedback gain on the steering angle, \(k_{2}\) denotes the weight of the motion state on the steering angle, \(k_{i}\) denotes the weight of the integral feedback gain on the steering angle, and \(I_{\text{int}}\) is the partial integral. A farming machine does not operate in a completely parallel section; it needs to perform turnaround steering to complete the whole section of the path. The focus of attention is on its speed and stability when turning and switching sections, and the automatic turning lies in identifying whether the farm machine has reached the boundary of the ground headland  
Figure 4: Fuzzy adaptive PD control simulation model. area, so the distance between the position of the farm machine and the boundary can be calculated and the distance result can be compared with the threshold value to carry out the command judgement.