# Trajectory Tracking Control Strategy of 20-Ton Heavy-Duty AGV Considering Load Transfer
## 5 Trajectory Tracking Co-Simulation Analysis Based on Simulink and CarSim
### Simulation Results Extraction and Analysis
#### 5.2.2 Trajectory Tracking Simulation Under Low Pavement Adhesion Coefficient  
The low-adhesion-coefficient pavement is used to simulate the trajectory tracking performance under the conditions of snowy, rainy, and slippery outdoor factory pavements. Since the adhesion coefficient of snow-covered pavements is 0.2, the pavement adhesion coefficient is set to 0.2. The prediction horizon and control horizon are set to 18 and 15, respectively. All the evaluation parameters and control strategy schemes are the same as those for the high-adhesion-coefficient pavement. The simulation results are shown in Table 4 and Figures 15-18.  
Figure 14: Adhesion rate curve of each wheel: (**a**) left front wheel; (**b**) right front wheel; (**c**) left rear wheel; (**d**) right rear wheel.  
As can be seen from Figures 15-17, the vehicle's tracking performance, pose error, and maximum lateral acceleration during corner entry/exit on the low-adhesion coefficient pavement are nearly identical to those on the high-adhesion coefficient pavement. According to Table 4, the maximum lateral acceleration of the IMPC controller is reduced by 19.7% compared with both the MPC and PID controllers. Therefore, the IMPC controller also achieves the goal of reducing lateral load transfer on low-adhesion coefficient pavements.  
As can be seen from Figure 18, on the low-adhesion coefficient pavement, during AGV startup and hill climbing, the TPD controller reduces the front wheel adhesion rate while increasing the rear wheel adhesion rate, and the maximum wheel adhesion rate is reduced, consistent with the high-adhesion coefficient pavement scenario. As shown in Table 4, the maximum wheel adhesion rate decreases by 11.6%, demonstrating effective torque distribution.  
In summary, the control strategy proposed in this paper effectively reduces load transfer while ensuring tracking accuracy on both high- and low-adhesion coefficient pavements, achieves optimal torque distribution, and improves AGV driving stability, demonstrating ideal control performance.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{**Control Strategy**} & \(1\epsilon_{X}\mathbf{l_{max}/m}\) & \(1\epsilon_{Y}\mathbf{l_{max}/m}\) & \(1\epsilon_{Y}\mathbf{l_{max}/m}\) & \(1\alpha_{y}\mathbf{l_{max}/(m/s^{2})}\) & \(C_{\mathbf{max}}\) \\ \hline PID & PID-TED & 0.2273 & 0.2419 & 0.0816 & 0.0502 & 0.8934 \\ \hline MPC & MPC-TED & 0.2947 & 0.2132 & 0.0808 & 0.0502 & 0.8871 \\  & MPC-TPD & 0.2947 & 0.2492 & 0.0823 & 0.0403 & 0.7847 \\ \hline IMPC & IMPC-TED & 0.2947 & 0.2492 & 0.0823 & 0.0403 & 0.8871 \\  & IMPC and PID & 29.7\% & 3.0\% & 0.9\% & \(-19.7\%\) & - \\ comparison & IMPC and MPC & 0 & 16.9\% & 1.9\% & \(-19.7\%\) & - \\  & TPD and TED & - & - & - & - & \(-11.5\%\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Simulation results under low pavement adhesion coefficient.  
Figure 15: Trajectory tracking curve.  
Figure 16: Tracking error curve: (**a**) \(X\)-axis direction error; (**b**) \(Y\)-axis direction error; (**c**) maximum yaw angle error.  
Figure 17: Lateral acceleration curve.