# Multi-Objective Collaborative Control Method for Multi-Axle Distributed Vehicle Assisted Driving
## 4 Simulation and Analysis
### Low Adhesion Road Simulation Conditions in Upper Layer  
The simulation of low adhesion roads is conducted on roads with an adhesion coefficient of 0.4, and the longitudinal speed of the vehicle is 15 m/s. Under this simulation condition, the driver has a strong willingness to independently control the vehicle. Figure 13c shows the torque results of the intelligent assistance system and the driver. Due to the inconsistency of the target paths between the driver and the intelligent assistance system, in order to maintain tracking of the auxiliary target path, the comparison strategy is inconsistent with the direction of the driver's efforts, resulting in significant torque conflicts. The driver needs to continuously increase the output of the steering torque \(T_{h}\) to ensure their own steering control over the vehicle. However, when t = 3 s, the proposed strategy can calculate the human-machine cooperation index \(CI\) in real-time based on the conflict caused by the torque between the human and machine and adjust the assisted driving weight adjustment coefficient \(\lambda_{r}\) in a timely manner through fuzzy logic control. As shown in Figure 13b, the assisted driving weight adjustment coefficient \(\lambda_{r}\) transitions smoothly from 0.97 to 0.03 in the range of 3-4 s, and the controller maximizes the transfer of control to the driver. Figure 13c shows that the torque of the driver under the comparison strategy reaches over 10 Nm, while the peak torque input of the driver under the proposed strategy control is only about 3 Nm, which can significantly reduce the operational burden of the driver and respect the driver's intention to operate. Meanwhile, as shown in Figure 13a, it can be observed that compared to the comparison strategy, the proposed strategy can ensure that drivers with autonomous control intentions can track the target path. Until the torque conflict between the human-machine disappears and the target path returns to consistency, the assisted driving weight adjustment coefficient \(\lambda_{r}\) gradually increases around t = 10 s. The intelligent assistance system regains high control until the next conflict occurs. In addition to its advantages in resolving human-machine conflicts, the proposed strategy can still ensure the handling stability of the vehicle. Comparison strategy B and the proposed strategy are selected for comparison in terms of vehicle dynamic control. The comparison strategy B is the same as the proposed strategy in path tracking and can solve human-machine collaboration problems. In terms of vehicle dynamic control, the comparison strategy B considers fixed-weight optimization of handling stability, which is the same as the comparison strategy. Based on Figure 12b,g, it can be observed that the proposed strategy only dynamically increases the stability weight adjustment coefficient \(\lambda_{\beta}\) around t = 5 s and t = 9 s, with the vehicle's stability control being the main focus. At other times, it can meet the tracking requirements for the ideal reference yaw rate of the vehicle. Meanwhile, Figure 13d shows that the proposed strategy, compared to comparison strategy B, eliminates the need for the driver to significantly adjust the steering to ensure vehicle control, greatly improving the driver's handling of the vehicle while ensuring stability. By comparing the path tracking effects of the two strategies in Figure 13a, it can be seen that  
Figure 12: Comparison of control effects for high adhesion road simulation conditions. (**a**) Path tracking results. (**b**) Weight adjustment coefficient. (**c**) Torque output comparison. (**d**) Steering angle. (**e**) Generalized additional yaw moment. (**f**) Vehicle sideslip angle. (**g**) The tracking effect of the proposed strategy on yaw rate. (**h**) The tracking effect of the comparison strategy on yaw rate. the proposed strategy can assist the driver in achieving higher accuracy and more stable path tracking effects, especially during the process of returning to the original lane.