# Event-Driven Dynamics Model of Operating State Evolution for Cantilever Roadheader
## 2 Dynamics Model of the State Evolution of Cantilever Roadheader
### Event-Driven Graph Construction of Operating State Evolution  
#### 2.2.1 Operating State Evolution Relationship and Graph Construction  
(1) Static Graph Construction  
Based on the cutting state discretization results shown in Figure 3, the equipment position will sequentially transition from state \(S_{A}\) to \(S_{H}\) under ideal working conditions. The inter-node relationships in the graph can be characterized by the following variations in the specific attitude parameters: when transitioning from \(S_{A}\) to \(S_{B}\), the cutter arm's rotating angle changes unidirectionally by \(\Delta\theta_{H}\); when transitioning from \(S_{B}\) to \(S_{C}\), the lifting angle changes by \(\Delta\theta_{T}\). Correspondingly, the transition between nodes \(S_{A}\) and \(S_{B}\) can be expressed as \(\theta_{H}+=\Delta\theta_{H}\), and between \(S_{B}\) and \(S_{C}\) as \(\theta_{T}+=\Delta\theta_{T}\). \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multirow{2}{*}{**Timestamp**} & \multicolumn{3}{c}{**Fuselage Position Coordinates**} & \multicolumn{3}{c}{**Fuselage Attitude Angles**} & \multicolumn{3}{c}{**Cutting Arm Attitude Parameters**} \\ \cline{3-10}  & & **Forward** & **Vertical** & **Lateral** & **Yaw** & **Pitch** & **Roll** & **Rotation** & **Lifting** & **Extension** \\ \hline Symbol & \(T\) & X & Y & Z & \(\alpha\) & \(\beta\) & \(\gamma\) & \(\theta_{H}\) & \(\theta_{T}\) & \(d\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: State parameters of the cantilever roadheader. Figure 2: Schematic of the operating state discretization. (2) Dynamic State Evolutionary Logic  
In the cutting process of the heading section, due to the complexity of the underground operating environment, the cutting process will inevitably encounter various disturbance events, which will have a certain impact on the cutting state, resulting in cutting abnormalities. For example, Figure 3(a) shows the schematic diagram of the normal fuselage posture, and Figure 3(b) shows the schematic diagram of the fuselage posture after sliding. In the cutting process from \(S_{A}\) to \(S_{B}\), the reaction force of the cutting head may cause the fuselage to slide sideways, and the changed fuselage position and attitude state of the cantilever roadheader cannot ensure optimal cutting quality according to the planned cutting trajectory. If the current fuselage slip event is regarded as an abnormal perturbation event, then the original fuselage attitude state evolution graph must be dynamically changed to ensure the feedback reliability of the graph. The abnormal perturbation occurs during the transition from state \(S_{A}\) to \(S_{B}\), so the relationship between \(S_{A}\) and \(S_{B}\) will be changed, and a new abnormal state node will be added between \(S_{A}\) and \(S_{B}\) due to the perturbation event. As shown in Figure 5, the planned state node at the moment before the anomalous state is generated will be recorded as the \(M_{1}\) intermediate state node, and, at the same time, \(M_{1}\) will be used as the target node for the correction of this anomalous state in order to ensure that the evolution of the state node returns to normal. During the intelligent cutting operations, abnormal disturbance events can cause the original cutting path to be disrupted at any time. In order to ensure the cutting quality of the heading section, adjustments must be made to restore the roadheader state to the  
Figure 4: Fuselage slippage of the cantilever roadheader. Figure 5: State branches in the state evolution graph. Figure 3: Static operating state evolution graph. intended route when the operation state is disturbed. In this context, the state evolution network of the heading workforce needs to realize closed-loop control when abnormal state branches appear, i.e., it automatically corrects the abnormal changes in the tunneling state caused by disturbances and returns to the planned operation path.