## 2 Materials and Methods
### Definition and Analysis of Path-Tracking Deviation Pattern
#### 2.2.1 Definition of Path-Tracking Deviation Patterns  
Based on the real data of navigation state quantities (without adding systematic measurement errors), each deviation pattern is divided according to the variation interval of the real data curve. 1. Classification of abnormal states  
In order to distinguish the rice transplanter path tracking deviation patterns, the navigation anomaly states are classified into three types, as shown in Table 3.  
Where \(P_{e\_max}\) is the maximum position deviation in the data curve, \(\varphi_{e\_max}\) is the maximum heading deviation in the data curve, and \(\beta\) is the sideslip angle in the data curve. 2. Classification of degree of oscillation  
In order to distinguish the categories of oscillatory states in a more detailed way, the degree of oscillation was classified into three types, as shown in Table 4.  
3. Classification of Degree of Sideslip  
In order to distinguish the categories of sideslip status in a more detailed way, the degree of sideslip was classified into three types, as shown in Table 5.  
2.2.2. Key Characteristic Variables of Path-Tracking Deviation Patterns  
In order to construct a dataset with significant features, the key feature variables under each deviation pattern are clarified by analyzing the dynamic correlation characteristics of each functional module in the simulation platform. 1. Key characterization variables in oscillation states  
When the rice transplanter did not sideslip, the change rule of the state variables conformed to the kinematic model. At this time, the rate of change of position deviation is the longitudinal speed of the rice transplanter about the target path. \[\dot{P}_{e}=v\cdot\sin\varphi_{e}, \tag{10}\]  
The rate of change in heading deviation is equal to the rate of change in heading. \[\dot{\varphi_{e}}=v\cdot\frac{\tan\delta_{f}}{l}, \tag{11}\]  
From Equations (10) and (11), combined with the classification rules of the path-tracking oscillation pattern, linear characteristics of \(P_{e}\), \(\varphi_{e}\), and \(\delta_{f}\) can be used to directly characterize whether oscillation occurs. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Degree of Oscillation** & **Classification Criteria** & **Label** \\ \hline Mild & 0.05 \(m<P_{e\_max}\leq\) 0.10 \(m\) & 1 \\ Moderate & 0.10 \(m<P_{e\_max}\leq\ 0.15m\) & 2 \\ Severe & 0.15 \(m<P_{e\_max}\) & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Rules for classifying the degree of oscillation. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Abnormal State** & **Classification Criteria** & **Label** \\ \hline Normal & \((P_{e\_max}<0.05\) m) and \((\varphi_{e\_max}<3^{\circ})\) & 1 \\ Oscillation & \((P_{e\_max}\geq 0.05\) m) or \((\varphi_{e\_max}\geq 3^{\circ})\) & 2 \\ Sideslip & \(\beta\geq 4\) & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Rules for classifying the abnormal states. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Degree of Sideslip** & **Classification Criteria** & **Label** \\ \hline Mild & \(4^{\circ}<\beta\leq 6^{\circ}\) & 1 \\ Moderate & \(6^{\circ}<\beta\leq 8^{\circ}\) & 2 \\ Severe & \(8^{\circ}<\beta\) & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Rules for classifying the degree of sideslip. Key characterization variables in sideslip states  
The rice transplanter sideslip process can be regarded as a navigation path tracking process with small angle changes in heading when \(P_{e}\) changes drastically and \(\varphi_{e}\) does not change significantly. From Equation (9), it can be seen that when \(\varphi_{e}\) changes very little, \(\delta_{f}\) is more sensitive about the response of \(P_{e}\), and in the process of sideslip, the relationship between the three changes is nonlinear; at this time, it can be based on this nonlinear feature to determine whether sideslip occurs. In summary, it can be clarified that the key characteristic variables of the deviation pattern of rice transplanter navigation path tracking are \(P_{e}\), \(\varphi_{e}\), and \(\delta_{f}\), respectively.