## 4 Results
### Simulation Experiment of Low-Attachment Double-Moving Line Condition  
The low-adhesion double-line-moving condition can simulate the lane-changing action of the vehicle on rainy and snowy days. The adhesion coefficient of the road is 0.3, and the vehicle speed is 60 km/h. The obtained simulation results are shown in Figures 10 and 11.  
Figure 10: Low attachment double shift line condition (**a**) Convergence process; (**b**) \(\beta-\hat{\beta}\) phase trajectory diagram.  
According to Figure 10a, the PSO found the optimal ITAE value of 33.5 when approaching 15 iterations in this experiment. According to the phase trajectory diagram shown in Figure 10b, it can be seen that the phase trajectories of the four control systems are located in the stable region. It can be seen that the phase trajectory of the MPC optimized by PSO  
Figure 11: Low attachment double shift line condition (**a**) Centroid sideslip angle; (**b**) yaw rate; (**c**) lateral tracking error; (**d**) tracking effect; (**e**) driving torque of each wheel.  
According to Figure 12a, the PSO found the optimal ITAE value of 37.25 when approaching 20 iterations in this experiment. According to the phase trajectory diagram shown in Figure 12b, it can be seen that the phase trajectories of the four control systems are located in the stable region, and it can be seen that the phase trajectory of the MPC optimized by PSO is more concentrated than that of the MPC without optimization. Therefore, the control strategy proposed in this paper improves the stability.  
Figure 13: Alt3 from the FHWA operating condition (**a**) Centroid sideslip angle; (**b**) yaw rate; (**c**) lateral tracking error; (**d**) tracking effect; (**e**) driving torque of each wheel.  
As shown in Figure 13a, the value of \(\beta\) of the proposed control system changes gently. It tends to be 0, with an average value of 0.00025 deg and a peak value of 0.01044 deg, which is the minimum value among all of the control systems, and the optimization effect is significant. In Figure 13b, the control strategy proposed in this paper has no noticeable difference compared to the other three control systems, and the average value is 0.234 deg/s. Regarding the tracking accuracy, the control system proposed in this paper is more accurate than the other three control systems, with an average value of 0.0015 m, which improves the accuracy of the trajectory tracking.  
Based on the above experimental results and analysis, the yaw rate and yaw angle are essential indicators for evaluating the vehicle's stability, representing the magnitude of the steering acceleration and the degree of body lateral deviation of the uncrewed vehicle when it moves laterally. The control system based on the PSO and phase diagram analysis designed in this paper effectively improves the accuracy and smoothness of the trajectory tracking while ensuring the vehicle's stability under limited working conditions, such as high speed and low adhesion. In the experiment, the controller designed in this paper has the problem of degradation in trajectory tracking accuracy. After the analysis, the reason for this is that the stability and trajectory tracking control interact at high and low speeds. The improvement of stability will affect the change in trajectory tracking accuracy, and the change in trajectory tracking accuracy will also affect the improvement of the stability. Through the method of PSO and phase diagram analysis, this paper takes stability and tracking accuracy as the comprehensive optimization objectives and obtains the results of bi-objective coordination optimization.