# Multi-Objective Collaborative Control Method for Multi-Axle Distributed Vehicle Assisted Driving
## 4 Simulation and Analysis
### Simulation Analysis of Torque Allocation in Lower Layer  
On the premise of ensuring that the control strategy in the upper layer adopts the proposed multi-objective MPC-assisted driving control algorithm, a comparative analysis of the torque allocation strategy in the lower layer is conducted, and the simulation conditions are consistent with the verification of the upper layer strategy. Figure 14 shows the torque allocation results of the proposed strategy and the comparison strategy on the left and right wheel motors of the vehicle under high adhesion conditions. Based on Figure 15, it can be observed that the two strategies have tracking errors for the virtual control variables of longitudinal force and yaw moment at around t = 5 s and t = 8 s, which is caused by the limitation of motor torque. At other times, they can basically achieve good tracking of their respective virtual control variables. At the same time, the actual tracking effects of the two strategies for generalized longitudinal force and generalized yaw moment are almost identical. Based on this, it is fair to conduct an optimization analysis involving tire load rate and driving system energy efficiency, and there will be no situation where the tracking effect is sacrificed to improve a certain performance. Figure 16 shows a comparison of tire load rate results corresponding to two torque allocation strategies. The increase in the stability weight adjustment coefficient of the proposed strategy at t = 5 s and t = 8 s and the improvement in the tire load rate optimization weight of the proposed torque allocation strategy significantly reduces the peak load rate of each tire at the corresponding time compared to the comparison strategy. In order to compare the tire load rate results of the two strategies more intuitively, their load rate cumulative distribution function (CFD) results are statistically analyzed separately. As shown in Figure 17, under high adhesion conditions, the proposed torque allocation strategy and the comparison strategy have a total tire load rate of less than 5.4 at 100% and 98.3% driving times, respectively. Under low adhesion conditions, the two strategies correspond  
Figure 14: The torque allocation results under high adhesion conditions. (**a**) Left motor torque of the proposed strategy. (**b**) Left motor torque of the comparison strategy. (**c**) Right motor torque of the proposed strategy. (**d**) Right motor torque of the comparison strategy. to a total tire load rate of less than 5.8 at 100% and 98.5% of driving times, respectively. It can be seen that the proposed torque allocation strategy has a better optimization effect on tire load rate compared to the comparison strategy, especially in times of high steering instability, which also indicates that it has a higher tire stability margin and is conducive to stable driving of the vehicle. Figure 18 shows the power loss comparison of the drive system under two strategies. As the proposed strategy can ensure that each wheel motor operates in high efficiency region as much as possible, it can achieve lower power loss most of the time. In order to compare the energy-saving effects of the two strategies, the instantaneous power loss under two operating conditions is integrated separately. Under high adhesion conditions, the energy consumption corresponding to the proposed torque allocation strategy and the comparison strategy are 0.1401 kWh and 0.152 kWh, respectively. Under low adhesion conditions, the energy consumption is 0.0924 kWh and 0.1006 kWh, respectively. Therefore, the proposed torque allocation strategy can achieve energy-saving effects of 7.86% and 8.13%, respectively, compared to the comparison strategy. Figure 16: Tire load rate under high adhesion conditions. (**a**) Left tire load rate of the proposed strategy. (**b**) Left tire load rate of the comparison strategy. (**c**) Right tire load rate of the proposed strategy. (**d**) Right tire load rate of the comparison strategy.