*4.3. Extreme Steering Condition*

In order to further reflect the control effect of optimal torque distribution, the extreme steering condition test was carried out. The four-axle reverse phase steering mode was adopted, with the first and second axles deflecting in the opposite direction to the third and fourth axles. The target speed of the vehicle was set to 10 km/h. At 20 s, the right wheel of the first axle deflected about 23◦ within 2 s, and the deflection angles of other wheels were calculated according to Ackerman steering principle, as shown in Figure 14a. For the change of speed, the vehicle speed after optimal control was still slightly higher than that under average distribution as shown in Figure 14b, which was the same as the previous simulation results. However, when the vehicle was in steady-state steering, the vehicle speed was basically unchanged compared with driving in the straight line, which indicates that the additional steering resistance was relatively small in this working condition.

**Figure 14.** Changes in vehicle driving parameters after the optimization control in reverse phase steering condition: (**a**) wheel deflection angle; (**b**) longitudinal vehicle speed.

As shown in Figure 15, the driving track of the vehicle remained unchanged basically after optimization. The steering radii of the vehicle after average distribution and optimal distribution were 8.1165 m and 8.1053 m respectively, which means that the optimal distribution of drive torque control did not have a great impact on the vehicle trajectory and body posture.

**Figure 15.** Comparison of vehicle trajectory and body posture under average distribution and optimal distribution.

Figure 16 shows the change of wheel drive torque. 0 s to 20 s was a linear acceleration phase, and the drive torque was distributed between the axles. Since the motor was in the state of low speed and low torque at this stage, in order to improve the overall working efficiency, the driving torque of the vehicle was mainly distributed to the first axle and the third axle to increase the workload of the motor. When entering the steering at 20 s, due to the increase of the driving resistance, the driving torque of the vehicle increased in order to maintain the target speed. However, when the vehicle was in steady-state steering, the drive torque was basically the same as that when the vehicle traveled in a straight line, which was caused by the reduction of driving resistance by the four-axle reverse phase steering. It can be seen that the optimization control made the distribution ratio of the outboard and rear axle wheels increase, which further promoted the reduction of driving resistance, thus achieving the purpose of reducing the driving energy consumption.

**Figure 16.** Comparison of wheel drive torque change under average distribution and optimal distribution.

When the vehicle was in steady-state steering, the total required drive torque of the vehicle with the average torque distribution was 1860.0376 Nm, and after the optimal distribution control, it was only 1656.6745 Nm, which was about 10.9332% lower. Then the change of the vehicle *SOC* during the steering phase was compared. The actual energy consumption decreased by about 13.3679%, which was much more obvious than the conclusion obtained by the above that maximum reduction in energy consumption is about 5%. This is mainly because the working efficiency of the motor is extremely low under low speed conditions [33]. Meanwhile, according to the motor efficiency map used in this paper, when the vehicle speed was lower than 30 km/h, the efficiency changed greatly with the torque, so the optimization control effect was better under this working condition. Besides, it was found that when other conditions were the same and four-axle reverse phase steering was adopted, the vehicle demand torque was far less than that when two-axle steering was adopted, sometimes less than half of that. Smaller drive torque led to lower working efficiency, which also led to the more obvious optimization effect.

### *4.4. Performance Evaluation*

It should be emphasized that the optimal distribution of drive torque control can achieve the maximum energy saving effect of about 5% in the conventional steering conditions, but it is only for the motor efficiency map used in the current paper (Figure 3). The motor efficiency map had a great influence on the actual optimization effect. If the high efficiency area of the in-wheel motor was small, the energy saving control effect on the vehicle was obvious. In addition, the selection of algorithm training conditions should be closer to the actual driving state of the vehicle, and enough training times should be ensured to make the parameters in the Actor network tend to the stable and optimal value.
