## 5 Results and Discussion
### Effectiveness of KA-DDPG  
In order to verify the control performance of the KA-DDPG-based torque distribution method for skid-steering vehicles, the simulations were designed with two different scenarios: a straight scenario and a corning scenario. The low-fidelity controller defined in Section 3.2.2 was considered as the baseline for comparative experiments, which is a controller based on physical knowledge. We introduced an evaluation method that is, commonly, used to quantitatively evaluate longitudinal speed and yaw rate tracking performance. This evaluation method uses the integral of the quadratic function of the tracking error of the longitudinal speed and yaw rate, to evaluate the tracking performance. The integrals \(J_{1}\) and \(J_{2}\) are, respectively, expressed as follows [41]:  
\[ \begin{split} J_{1}&=\int_{0}^{t}\upsilon_{delta}^{2 }\,d\tau,\\ J_{2}&=\int_{0}^{t}\omega_{delta}^{2}\,d\tau.\end{split}  \tag{23}\]  
In the straight scenario, the desired yaw rate was always kept at 0 rad/s, in order to identify the drift of the skid-steering vehicle. The desired longitudinal speed changed during the simulation, which was set to 3.8 m/s at the beginning of the simulation, to 1.8 m/s and 3.2 m/s at 200 s and 400 s, respectively, and, then, kept at 3.2 m/s until the end. The simulation results for the straight scenario are shown in Figure 8.  
Figure 8a shows a comparison of longitudinal speed tracking, for the different torque distribution methods in the straight scenario. To more clearly demonstrate the tracking performance for longitudinal speed, Figure 8b shows the corresponding tracking error. The tracking error of the baseline method fluctuated greatly, and the longitudinal speed tracking performance was significantly worse than that of KA-DDPG. The tracking error of the baseline frequently exceeded 0.2 m/s, while the maximum error of KA-DDPG was always stably kept within 0.2 m/s. Figure 8c shows a comparison of the yaw rate tracking performance in the straight scenario. It can be emphasized that the target yaw rate is a constant value in the straight scenario, which is always 0 rad/s. The tracking results show that KA-DDPG kept the tracking error of the yaw rate within 0.2 rad/s, while the maximum tracking error of the baseline exceeded 0.2 rad/s. As shown in Figure 8d, the heading of the baseline was larger than that of KA-DDPG, indicating that the vehicle controlled by the baseline suffered from greater drift. These simulation results demonstrate that the tracking performance of the KA-DDPG algorithm, for the longitudinal speed and yaw rate in the straight scenario, was better than that of the baseline. Figure 9 shows the torque distribution curves for each wheel in the straight scenario, and the torque distributions of the two different methods had similar trends. However, the driving torques of the KA-DDPG algorithm reflect the vehicle's situation more quickly than the baseline, which explains why the KA-DDPG algorithm presented better tracking performance than the baseline. To verify the cornering ability of the KA-DDPG-based torque distribution method, the simulations were conducted in a cornering scenario. Compared to the simulations in the straight scenario, the tracking performance of the proposed torque distribution method was more rigorously verified in the cornering scenario. The longitudinal speed of the vehicle was set to 1.8 m/s at the beginning of the simulation, 3.7 m/s at 150 s, 2.5 m/s at 350 s, and, then, held at 2.5 m/s until the end. The yaw rate was no longer a constant value, which was set to 3.2 rad/s at the beginning of the simulation, 2.5 rad/s at 150 s, 3.7 rad/s at 350 s, and, then, held at 3.7 rad/s until the end of the simulation. The tracking performances of the different methods in the cornering scenario are shown in Figure 10. Figure 10a shows the longitudinal speed tracking results in the cornering scenario, and it can be seen, intuitively, that the longitudinal speed tracking performance did not deteriorate significantly, compared with the straight scenario.