# Mass Estimation-Based Path Tracking Control for Autonomous Commercial Vehicles
## 4 Algorithm Verification
### Simulation Verification
#### 4.1.2 Controller Simulation Analysis  
Through the joint simulation of MATLAB/Simulink and TruckSim, the effectiveness and superiority of the introduced path tracking controller are confirmed. The simulation vehicle model selected is the large European van, with basic vehicle parameters as shown in Table 2.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value** & **Unit** \\ \hline Vehicle length & 5.995 & m \\ Vehicle width & 2.18 & m \\ Moment of inertia \(I_{z}\) & 4245 & kg\(\cdot\)m\({}^{2}\) \\ Distance from center of mass to front axle \(I_{f}\) & 1.20 & m \\ Distance from center of mass to rear axle \(I_{r}\) & 2.108 & m \\ Front wheel camber stiffness \(C_{f}\) & 170,000 & N/rad \\ Rear wheel camber stiffness \(C_{r}\) & 170,000 & N/rad \\ Discrete time \(T_{s}\) & 0.01 & s \\ Steering ratio \(i\) & 22 & \\ Prediction domain \(N_{p}\) & 40 & \\ Control domain \(N_{c}\) & 40 & \\ State vector weight matrix & Diag[3,0,40,0,10] & \\ Control weight & 8 & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Main kinematic parameters of the vehicle.  
Figure 6: Mass estimation simulation result graph; (**a**) Unloaded mass estimation; (**b**) Half-load mass estimation; (**c**) Full-load mass estimation.  
The standard double-lane change test condition was selected for testing, where the road was set as a wet and slippery low-adhesion surface. In the actual control program, all controller weight parameters were the optimal parameters from simulation. To evaluate the controller's performance under rigorous conditions, the vehicle's speed was set to 50 km per hour within the simulation environment, and the corresponding results are illustrated in Figure 6.  
Figure 7a shows the tracking effects of three different controllers on vehicle control under double-lane change conditions. From the magnified view, it can be seen that the model predictive control with mass estimator tracks most accurately and stably follows the reference curve. Both the MPC controller and LQR controller exhibit varying degrees of deviation during steering. Figure 7b represents the lateral errors of the three controllers. The MFFRSL + MPC controller has the smallest lateral error, with a maximum lateral error of only \(-0.03\) m. In contrast, the MPC controller's lateral error fluctuates significantly during turning, with a maximum lateral error reaching \(-0.07\) m, which is due to inaccurate mass parameters leading to model mismatch. The LQR controller has a maximum lateral error of \(-0.08\) and also exhibits steady-state error at the end. Figure 7c presents the heading errors of the three controllers. The MFFRSL + MPC controller performs best in terms of heading error, with the largest heading error occurring at the first peak, which is 0.04 rad. The LQR controller performs the worst, with a maximum heading error of \(-0.07\) rad. The MPC controller's maximum heading error is 0.05 rad. Figure 7d illustrates the performance of the steering wheel angle for the three controllers. The MFFRSL + MPC controller maintains a stable steering wheel angle with a quick response. This is because the MFFRSL + MPC controller model takes into account the disturbances caused by load changes and can also achieve feedback correction within the prediction horizon. In contrast, the MPC controller exhibits unstable steering wheel jitter, while the LQR controller responds slowly.  
Figure 7: Comparison of controller simulation results: (**a**) Path tracking effect comparison; (**b**) Lateral error; (**c**) Heading error; and (**d**) Steering angle.