## 5 Simulation and Discussion
### Docking Road Driving Simulation  
The joint road is set with the first half having an adhesion coefficient of 0.5 on a slippery asphalt road, and the second half having an adhesion coefficient of 0.18 on a compacted snow road. The simulation speed accelerates from 0 km/h to 70 km/h within 10 s, with the optimal slip ratio being 0.18 in the first half and 0.12 in the second half. Figure 7 shows the estimation results and errors of the adhesion coefficient on the joint road. The analysis reveals that, similar to the split road scenario, the adhesion coefficient converges to a value close to the true value within 1 s of vehicle start-up. Due to the sudden change in the road adhesion coefficient at the 5 th second, the estimated value also changes abruptly, resulting in a significant estimation error at this point. After the road adhesion coefficient changes, the estimated value stabilizes again. Compared to the UKF, the AUKF still demonstrates excellent performance on the joint road. Table 3 shows the average estimation error on the joint road. The analysis shows that the average estimation error of the AUKF is reduced by 69% compared to the UKF, indicating a significant improvement in estimation performance. Figure 6: Simulation results of acceleration on split road. (**a**) Wheel slip ratio without control. (**b**) Wheel slip ratio under CESMC control. (**c**) Wheel slip ratio under DASMC control. (**d**) Wheel torque under CESMC control. (**e**) Wheel torque under DASMC control. (**f**) Vehicle speed comparison under different controls. Figure 8 shows the simulation results for the joint road scenario. Since the simulation results for the left and right wheels are almost identical, the analysis focuses on the left front wheel and right rear wheel. As shown in Figure 8a, due to the relatively better adhesion coefficient in the first half of the road, the rear wheels start to slip and lose stability after 5 s, but the first 5 s do not fully utilize the road adhesion coefficient. Figure 8b,c indicate that after the intervention of both control algorithms, the slip ratio under CESMC control experiences severe chattering due to the sudden change in road conditions, especially at the transition between the two adhesion coefficients. The overshoot for both front and rear wheels in the first half reaches 0.34, with the steady-state time between 0 and 3 s. At the transition, the overshoot is around 0.1, with the steady-state time between 5 and 7 s. With the DASMC control algorithm, the initial overshoot is controlled within 0.08, with a steady-state time within 1 s. At the road transition, the overshoot is almost reduced to 0, with a response time within 0.1 s. The rear wheel control shows a slight delay due to the vehicle's length. The results demonstrate that the improved algorithm can quickly respond to sudden changes in conditions, effectively reducing chattering and steady-state errors, promptly controlling when there are significant errors, and avoiding over-control when there are minor errors, indicating good disturbance resistance. Figure 8d,e show that the motor torque under DASMC control can quickly, smoothly, and stably apply the anti-slip control torque to each wheel, significantly improving over traditional equivalent control. The speed curve in Figure 8f shows that without control, the vehicle speed can barely track \begin{table}
\begin{tabular}{c c} \hline \hline
**Estimation Strategy** & **Condition1 (L)** \\ \hline UKF & 0.0660 \\ AUKF & 0.0201 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Average estimation error on joint road. Figure 7: Simulation results of acceleration on split road. Simulation estimation results for joint road. (**a**) Adhesion coefficient estimation results. (**b**) Estimation error. up to 45 km/h within 0 to 5 s. With CESMC control, the speed tracking improves, and the speed fluctuations at the transition reduces, but the final speed only reaches 59 km/h.