# Multi-Objective Collaborative Control Method for Multi-Axle Distributed Vehicle Assisted Driving
## 4 Simulation and Analysis
### High Adhesion Road Simulation Conditions in Upper Layer Steering Angle  
The simulation of high-adhesion roads is conducted on roads with an adhesion coefficient of 0.8, and the longitudinal speed of the vehicle is 20 m/s. Both the driver and the intelligent assistance system have their own target paths. The driver target is to drive in a straight line, while the intelligent assistance system target is to perform dual lane change (DLC). At the same time, the driver's willingness to control the vehicle is relatively low under this condition. The torque input of the driver in Figure 12c is maintained at a relatively low level, which results in the proposed strategy's assisted driving weight adjustment coefficient \(\lambda_{r}\) based on fuzzy rules approaching 1 (as shown in Figure 12b). At this point, the auxiliary systems under both strategies have high driving control rights, and the auxiliary component \(T_{a2}\) by the steering motor has absolute control over the vehicle's steering. As shown in Figure 12a, both of them can complete the tracking of the target path of the intelligent assistance system. In terms of vehicle dynamics control, the proposed strategy proposes a handling stability collaborative control method, which dynamically adjusts the stability weight adjustment coefficient \(\lambda_{\beta}\) for different conditions during vehicle operation. The results are shown in Figure 12b. Based on the steering angle results in Figure 12d, it can be observed that most of the time, \(\lambda_{\beta}\) remains at a low value, and vehicle dynamic control prioritizes vehicle handling stability. And near \(t=5\) s and \(t=8\) s, as the vehicle's steering angle increases, there is a risk of vehicle instability, and the corresponding \(\lambda_{\beta}\) will rapidly increase, with stability control being the dominant factor. The comparison strategy comprehensively considers the handling and stability of the vehicle. By comparing Figure 12g,h, it can be seen that the proposed strategy has a good yaw rate tracking effect by adjusting the generalized additional yaw moment \(M_{d}\) when there is no risk of vehicle instability. To balance stability, the comparison strategy sacrifices a certain degree of yaw rate tracking performance, which is particularly evident during the first peak of the steering angle. This also makes it necessary for the comparison strategy to maintain the path tracking by increasing the steering angle input during the DLC tracking process. It can be observed from Figure 12d that the proposed strategy has smoother steering angle changes and smaller peak values compared to the comparison strategy, and the proposed strategy has better tracking performance and corresponding better driving experience. As shown in Figure 12f, although the sideslip angles of both strategies meet the stability constraints of \(|\beta|\leq\arctan(0.02\) \(\mu\)g), it is evident that the proposed strategy has higher vehicle stability. In summary, the proposed strategy can better solve the collaborative control of vehicle handling stability. Figure 11: The simulation model diagram. Figure 12: _Cont._