## 5 Tests and Performance Comparison
### Tests and Comparison of the nomRL-PFC and the \(\mu\)-randRL-PFC
Here, it can be seen that both agents achieve a reasonable performance with the nomRL-PFC offering a slightly better one since it tracks the reference path more closely with \(\left|e_{y}^{\text{P}}\right|<0.024\) m in this section. However, the path-following performance of the nomRL-PFC in this part of the path decreases significantly for \(\mu=0.6\), which can be seen in Figure 14. Here, it can be observed that the nomRL-PFC now makes greater position errors up to \(\left|e_{y}^{\text{P}}\right|\approx 0.06\) m and that it does not follow the path as closely as it did under dry  
Figure 12: Pathways of the nomRL-PFC (blue lines) and the \(\mu\)-randRL-PFC (orange line) on the road section around the arc length \(s=493\) m with the friction value \(\mu=0.6\). The reference path is represented by the black dashed line, whereas the path boundaries are depicted by the black solid lines. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{1}{c}{**Friction Value**} & \multicolumn{2}{c}{\(\mu\) = 0.6} & \multicolumn{2}{c}{\(\mu\) = 1.0} \\ \hline
**Agent** & **nomRL-PFC** & **\(\mu\)-randRL-PFC** & **nomRL-PFC** & **\(\mu\)-randRL-PFC** \\ \hline \(e_{y}^{\text{P}}\) [m] (RMS) & 0.033 & 0.011 & 0.013 & 0.013 \\ \(e_{y}^{\text{P}}\) [m/s] (RMS) & 0.114 & 0.171 & 0.106 & 0.150 \\ \(e_{y}^{\text{P}}\) [rad] (RMS) & 0.022 & 0.020 & 0.020 & 0.022 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The RMS errors of nomRL-PFC and \(\mu\)-randRL-PFC during the evaluation on the training path for the friction values \(\mu=0.6\) and \(\mu=1.0\). The best metric is highlighted green. road conditions (\(\mu=1.0\)). Furthermore, the \(\mu\)-randRL-PFC offers good position tracking performance with \(\left|e_{y}^{\mathrm{P}}\right|<0.02\) m for \(\mu=0.6\) (cf. Figure 14). Furthermore, in Table 3, it can be seen that the nomRL-PFC outperforms the \(\mu\)-randRL-PFC in terms of tracking the demanded velocity. For both friction values, the \(\mu\)-randRL-PFC generates a higher RMS of \(e_{v_{x}}^{\mathrm{P}}\) over the entire path. This can be explained by the hierarchical design of the reward function. It prioritizes the minimization of the position error before rewarding small velocity errors. This prioritization motivates the \(\mu\)-randRL-PFC to apply a rather conservative velocity tracking performance for all friction values as a trade-off for good position tracking. Therefore, the agent trained with friction randomization applies a slower velocity for the different friction values in order to track the position more successfully for any given friction value \(\mu\in[0.6,\ 1.0]\). Figure 14: The position error \(e_{y}^{\mathrm{P}}\) of the nomRL-PFC (blue line) and the \(\mu\)-randRL-PFC (orange line) on the road section between the arc lengths \(s=300\) and \(s=600\) for the friction value \(\mu=0.6\). Figure 13: The position error \(e_{y}^{\mathrm{P}}\) of the nomRL-PFC (blue line) and the \(\mu\)-randRL-PFC (orange line) on the road section between the arc lengths \(s=300\) and \(s=600\) for the friction value \(\mu=1.0\). It can be stated that the randomization of the road-tire friction during training increases the robustness of the agent. The performance of the \(\mu\)-randRL-PFC stays at a high level, whereas the performance of the nomRL-PFC steadily decreases for smaller \(\mu\).