# The Full-Field Path Tracking of Agricultural Machinery Based on PSO-Enhanced Fuzzy Standley Model
## 3 PSO-Enhanced Fuzzy Stanley Model  
### Principle of PSO Optimization  
PSO is a heuristic swarm intelligence algorithm, which stems from the research on the predation behavior of bird flocks [31]. In order to find the place where most food is located, the flocks adjust their search directions by using their own experience and communication among the flocks. Because of its fast convergence speed, easy online implementation and simple principle, it is widely used in the fields of fuzzy control system design and other high-dimensional optimization problems [32]. In the application of intelligent agricultural machinery for full-field unmanned operation, the various operation speeds, soil conditions and actuator saturation of steering control system will have a great effect on the accuracy and stability of path tracking. Therefore, in order to improve the adaptively of fuzzy-based SM, the PSO algorithm is employed to further optimize the expected steering angle.  
The steering control system of agricultural machinery is a closed-loop PID control system including an electric steering wheel, a mechanical steering mechanism and angle sensor fixed on the front wheel. It is easy to understand that when the driving speed is high, the steering wheel control input should be changed slowly and a small steering angle should be given. In order to handle the time-varying speed, PSO is employed to optimize the output gain of FSM. Define a control gain coefficient \(\alpha\), and the control gain of FSM is multiplied by the coefficient  
\[\delta_{PSO}(t)=\alpha\cdot\delta(t) \tag{7}\]  
where \(\delta_{PSO}(t)\) is the desired front wheel angle after utilizing PSO.  
When the speed of the agricultural machinery is high, the value of the coefficient \(\alpha\) should be reduced to improve the stability of the control. What is more, the steering control systems of the wheeled mobile vehicle and combine harvester involved in our work are actually a first-order system with time delay, and the varying parameters of the closed-loop PID will have a great effect on the navigation control decision. When the mobile robot is  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{\(\theta_{e}\)} & \multicolumn{8}{c}{_e_} \\ \cline{2-9}  & **NB** & **NM** & **NS** & **ZO** & **PS** & **PM** & **PB** \\ \hline NB & PS & PS & PS & PM & PB & PB & PB \\ NM & PM & PS & PS & PS & PM & PB & PB \\ NS & PM & PM & PS & PS & PM & PM & PB \\ ZO & PM & PM & PS & PS & PS & PM & PM \\ PS & PB & PM & PM & PS & PS & PM & PM \\ PM & PB & PB & PM & PS & PS & PS & PM \\ PB & PB & PB & PB & PM & PS & PS & PS \\ \hline \hline \end{tabular}
\end{table}
Table 1: Rule base for fuzzy logic control.  
subject to its steady-state stage of path tracking, i.e., at the end of a straight line tracking, the actuator saturation of the steering control system will make it difficult to respond to the large, expected input angle in a timely manner. However, by multiplying the expected steering angle by a coefficient \(\alpha\), the response speed of the steering control system can be improved, and thus the accuracy of the path tracking during the path transition period can be ensured.