## 4 Analysis of Control Strategy Based on Steering Stability
### Development of an Integrated Control Strategy Considering Steering Safety  
According to the operating environment of the tracked vehicle, the road conditions are: \(f=0.1\); \(\mu_{\max}=0.8\); \(\psi=0.9\) and when \(\alpha=0^{\circ}\), the critical speed-steering radius and steering angular velocity relationships under the influence of skidding and rolling are as shown in Figures 6 and 7.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Value** & **Unit** \\ \hline Tracked vehicle overall mass \(G\) & 2800 & kg \\ High quality core \(h\) & 1.15 & m \\ Track center distance \(B\) & 1.25 & m \\ Crawler ground length \(L\) & 1.56 & m \\ Drive wheel radius \(r\) & 0.18 & m \\ Variable Pump Displacement & 0–71 & mL/r \\ Hydraulic system pressure & 30 & Mpa \\ Motor Displacement & 514 & mL/r \\ Maximum pressure of fixed motor & 31.5 & Mpa \\ \hline \hline \end{tabular}
\end{table}
Table 1: Main parameters of the tracked vehicle.  
On the basis of Figures 6 and 7, at the same steering angular velocity, it can be seen that the critical speed under the rollover condition is always lower than the critical speed under the skidding condition. Therefore, only the relationship between critical speed and steering angular velocity under the rollover condition needs to be considered. When \(\alpha\
eq 0^{\circ}\), the research objective is the steering control of the tracked vehicle under travelling conditions that are longitudinal along the slope and along the contour line.  
On the basis of the analysis of the rollover conditions mentioned above, and considering the steering rollover control strategy of a tracked vehicle under different slopes, the control surfaces are calculated and fitted, as shown in Figure 8, for steering a tracked vehicle longitudinally along the slope and steering up and down the slope, respectively, along the contour line under different slope degrees (\(\alpha=0\)-\(30^{\circ}\)). The slope degree \(\alpha\) can be detected using an angle sensor in the actual situation. Figure 8a presents the control surface for rollover condition under longitudinal travel along the slope; Figure 8b presents the control surface for the rollover condition under travel along the contour line turning up the slope; Figure 8c presents the control surface for the rollover condition under travel along the contour line turning down the slope.  
Figure 6: \(v-R\) target curve under skidding conditions.  
Figure 7: \(v-\omega\) target curve under rollover conditions.  
According to the fitting relationship in Figure 8, the control strategy rule for the safety condition preventing rollover during steering is obtained as follows:  
\[\omega=\left\{\begin{array}{c}1(v\leqslant 0.6)\\ \left\{\begin{array}{c}v+0.4\Big{(}0.6<v\leqslant\frac{-0.4+\sqrt{0.16+23.52 \cos a}}{2}\Big{)}\\ \frac{5.88\cos\alpha}{v}\Big{(}\frac{-0.4+\sqrt{0.16+23.52\cos a}}{2}<v\leqslant 3.3\Big{)}\\ \left\{\begin{array}{c}v+0.4\Big{(}0.6<v\leqslant\frac{-0.4+\sqrt{0.16+(23.52 \cos a\pm 39.2\sin a)}}{2}\Big{)}\\ \frac{5.88\cos\alpha\pm 9.8\sin a}{v}\Big{(}\frac{-0.4+\sqrt{0.16+(23.52\cos a\pm 39.2 \sin a)}}{2}<v\leqslant 3.3\Big{)}\end{array}\right.\end{array}\right.\end{array} \tag{18}\]  
Figure 8: Slope steering driving roll control surface: (**a**) steering roll control surface for longitudinal driving along the slope; (**b**) roll control surface for turning uphill along the contour line; (**c**) roll control surface for steering downhill along the contour line.  
On the basis of the above analysis, the control rules are written using the S-function in MATLAB, corresponding to the \(v-w\) module in Figure 5, the control objectives of which are vehicle speed and steering angular velocity.