# 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  
#### 5.2.1 Trajectory Tracking Simulation Under High Payement Adhesion Coefficient  
High adhesion coefficient pavement is used to simulate the trajectory tracking performance of the AGV under dry outdoor factory pavement conditions. For dry asphalt or concrete pavements, the adhesion coefficient ranges from 0.8-0.9 [38]. With the mid-value selected, the pavement adhesion coefficient is set to 0.85. The prediction horizon and control horizon are set to 18 and 15, respectively. The evaluation parameters are extracted, including the maximum pose error \(\left.\right|_{\mathcal{E}}\)\(\left.\right|_{\mathcal{\max}}\) in the \(X\)-axis direction, the maximum pose error \(\left.\right|_{\mathcal{E}}\)\(\left.\right|_{\mathcal{\max}}\) in the \(Y\)-axis direction, the maximum yaw angle error \(\left.\right|_{\mathcal{\max}}\), the maximum lateral acceleration \(\left.\right|_{\mathcal{\max}}\) and the maximum wheel adhesion rate \(C_{\max}\), as shown in Table 3. The simulation results of the trajectory tracking curve, tracking error, lateral acceleration, wheel adhesion rate, and total driving torque of the front and rear wheels are shown in Figures 11-14. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Name** & **Trajectory Tracking Method** & **Torque Distribution Method** \\ \hline PID-TED & PID & Torque Equal Distribution \\ MPC-TED & MPC & Torque Equal Distribution \\ IMPC-TED & IMPC & Torque Equal Distribution \\ MPC-TPD & MPC & Torque Proportional Distribution \\ IMPC-TPD & IMPC & Torque Proportional Distribution \\ PID-TED & PID & Torque Equal Distribution \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Different control strategies. Figure 10: Reference trajectory. As can be seen from Figures 11 and 12, since the reference vehicle speed remains constant while the actual vehicle speed starts from zero, a relatively large position tracking error occurs in the initial tracking stage. However, the control strategies using the MPC and IMPC controllers can quickly reduce the error. When the vehicle reaches the circular arc section, the reference wheel angle changes suddenly. To ensure the smooth change in the system control variables, the actual wheel angle increases gradually rather than suddenly, which leads to a certain pose tracking error during cornering. Nevertheless, the MPC and IMPC controllers can also quickly reduce the error. In contrast, the PID controller has a poorer performance. It can be seen from Table 3 that the control strategy using the IMPC controller has a slightly larger maximum tracking error compared with that using the MPC controller. This is because the IMPC controller considers the limitation of load transfer in the objective function, sacrificing a certain tracking accuracy. However, the control accuracy still meets the usage requirements. As can be seen from Figure 13, a certain lateral acceleration is generated when the AGV is cornering. Since the steering angle of the AGV changes rapidly when entering and exiting the curve, there are certain extreme values of acceleration during these periods. As shown in Table 3, compared with the control strategy using the MPC controller, the maximum lateral acceleration of the control strategy using the IMPC controller is reduced by 22.40%. Compared with the control strategy using the PID controller, the maximum  
Figure 11: Trajectory tracking curve. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{**Control Strategy**} & \(\mathbf{l}\varepsilon_{X}\mathbf{l_{max}/m}\) & \(\mathbf{l}\varepsilon_{Y}\mathbf{l_{max}/m}\) & \(\mathbf{l}\varepsilon_{X}\mathbf{l_{max}/m}\) & \(\mathbf{l}\boldsymbol{y}\mathbf{l_{max}/(m/s^{2})}\) & \(\boldsymbol{C_{\max}}\) \\ \hline PID & PID-TED & 0.2272 & 0.2419 & 0.0816 & 0.0502 & 0.2102 \\ \hline MPC & MPC-TED & 0.2947 & 0.2132 & 0.0808 & 0.0502 & 0.2087 \\  & MPC-TPD & & & & & 0.1846 \\ \hline IMPC & IMPC-TED & 0.2947 & 0.2492 & 0.0823 & 0.0403 & 0.2087 \\  & IMPC-TPD & & & & & 0.1846 \\ \hline \hline \end{tabular}
\end{table}