## 2 Materials and Methods
### Analysis of Classis Stability Architecture  
We used the yaw rate, centroid slip angle, and wheel slip rate as control variables. A combination of the sliding mode control algorithm and the fuzzy PID control algorithm served as the main framework for the drive coordination control strategy. Additionally, a speed-following control was integrated to enable the sprayer to calculate the required drive torque and adjust the yaw moment based on control commands, ensuring that the wheel slip rate would not exceed the limit. Finally, the torque optimal distribution algorithm  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter Name** & **Parameter Unit** & **Description** \\ \hline \hline \begin{tabular}{c} Chassis drive form \\ Steering form \\ Vehicle from center of mass to front axis \\ \end{tabular} & \begin{tabular}{c} / \\ kg \\ mm \\ \end{tabular} & \begin{tabular}{c} Four-wheel independent motor drive \\ Four-wheel independent motor steering \\ \end{tabular} \\ \begin{tabular}{c} Distance from center of mass to front axis \\ \end{tabular} & \begin{tabular}{c} mm \\ \end{tabular} & \begin{tabular}{c} 900 \\ 700 \\ \end{tabular} \\ \begin{tabular}{c} Distance from center of mass to rear axis \\ \end{tabular} & \begin{tabular}{c} mm \\ \end{tabular} & \begin{tabular}{c} 1200 \\ 600 \\ \end{tabular} \\ \begin{tabular}{c} Maximum working speed \\ \end{tabular} & \
\begin{tabular}{c} km/h \\ \end{tabular} &
\begin{tabular}{c} 20 \\ 3 \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table}
Table 1: Results of the spray boom overall height adjustment test.  
allocated torque to each wheel, resulting in a driving stability control system for the sprayer. This system ensured that the sprayer would closely approach or even reach the desired state to maintain stable driving.  
The overall control process for the sprayer chassis stability control strategy studied in this paper was as follows:  
1. Determine the vehicle stability based on control signal commands and the current operating state of the sprayer to decide whether stability control intervention is needed.
2. If the vehicle is deemed stable, perform speed-following control alone by adjusting the sprayer's acceleration through the speed-following controller to match the desired speed. If instability is detected, calculate the expected stability-related parameters from the ideal two-degree-of-freedom model (the centroid slip angle and the yaw rate) and determine the deviation from actual parameters. Adjust the drive torque of each wheel based on the deviation to generate a yaw moment that ensures stable driving. Simultaneously, monitor the wheel slip rate, and if any wheel exceeds the acceptable slip rate range, correct the torque of the affected wheel to prevent the loss of directional control.
3. Finally, use the allocation algorithm of the lower-level controller to reasonably distribute the longitudinal drive torque and the adjustment torque output by the upper-level controller to each wheel, thereby achieving the stability control of the sprayer chassis.  
Based on the above analysis, the chassis stability control strategy of this paper is shown in Figure 3. The stability control system mainly consisted of a two-degree-of-freedom reference model, an instability judgment module, an upper-layer torque control module, and a lower-layer torque distribution module. After determining the overall architecture of the chassis stability control strategy, a detailed analysis of the entire system yielded the refined stability control strategy shown in Figure 4.  
Figure 3: The overall structure of chassis stability control strategy.