# Reinforcement Learning for Semi-Active Vertical Dynamics Control with Real-World Tests
## 6 Real-World Test
### Results from the Four-Post Test Rig
The obtained results are listed in Table 4 and depicted as a pareto plot in Figure 14.  
Figure 14 summarizes the test results in a pareto plot: All markers in the left bottom quadrant represent an excitation in which the RL agent performed better in both the road-holding as well as the adapted comfort metric. All markers with a road-holding criterion greater than 1 correspond to an excitation where the RL agent performed worse. Accordingly, markers with an adapted comfort criterion greater than 1 represent an excitation where the agent performed worse. The subplots of Figure 14 depict the metrics on different excitation types. Remark: Due to a corrupted measurement, the metrics for the road type B are missing on the synchronous road excitations. \begin{table}
\begin{tabular}{l l c c} \hline \hline \multicolumn{1}{c}{**Excitation**} & \multicolumn{1}{c}{**Type**} & \multicolumn{1}{c}{
\begin{tabular}{c} **Adapted ISO 2631** \\ **Comfort Criterion** \\ \end{tabular} } & \multicolumn{1}{c}{**Road-Holding Criterion**} \\ \hline Exponential Sine-Sweep (1–30 Hz \(\mid\)50 mm/s) & Sweep & 0.971 & 1.017 \\ \hline Exponential Sine-Sweep (1–30 Hz \(\mid\)100 mm/s) & Sweep & 1.019 & 1.028 \\ \hline Exponential Sine-Sweep (1–30 Hz \(\mid\)150 mm/s) & Sweep & 1.083 & 0.921 \\ \hline Exponential Sine-Sweep (1–30 Hz \(\mid\)200 mm/s) & Sweep & 1.108 & 0.871 \\ \hline Exponential Sine-Sweep (1–30 Hz \(\mid\)250 mm/s) & Sweep & 1.092 & 0.842 \\ \hline ISO 8608 Type A Road (asynchronous) & Road-like & 0.931 & 0.954 \\ \hline ISO 8608 Type B Road (asynchronous) & Road-like & 0.967 & 0.980 \\ \hline ISO 8608 Type C Road (asynchronous) & Road-like & 0.998 & 0.993 \\ \hline ISO 8608 Type D Road (asynchronous) & Road-like & 1.024 & 0.991 \\ \hline ISO 8608 Type A Road (synchronous) & Road-like & 0.947 & 0.943 \\ \hline ISO 8608 Type C Road (synchronous) & Road-like & 0.993 & 0.995 \\ \hline ISO 8608 Type D Road (synchronous) & Road-like & 1.032 & 0.991 \\ \hline Real Road Replay: Rough Bump & Road-like & 0.924 & 0.982 \\ \hline Real Road Replay: Rough Road & Road-like & 0.962 & 0.992 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Normalized performance metrics of the trained controller on different excitations. Metrics smaller than 1, depicted in green, indicate a superior performance of the RL agent; metrics greater than 1, depicted in red, represent a superior performance of the benchmark controller (compare [20]). Figure 14a shows that the RL-based controller can improve the road-holding for the sweeps with a zero-crossing velocity \(\geq\) 150 mm/s but thereby deteriorates the comfort criterion. For the sweep with a 50 mm/s zero-crossing velocity, the RL agent can improve the comfort but deteriorates the road-holding. Finally, for the excitation with 100 mm/s, the benchmark controller outperformed the RL agent on both metrics. In contrast, Figure 14b-d reveal that the RL agent was able to improve the road-holding metric for all examined road-like excitations. Apart from two exceptions, the trained controller also outperformed the benchmark controller in the adapted ISO 2631-1 comfort criterion. In Figure 14b,d, the two excitations where the trained controller could only improve the road-holding metric were, in both cases, the road type D, which corresponded to an unpaved road [45]. Additionally, Figure 14b,d also show that the trained controller performed worse with a decreasing road quality. Nevertheless, the trained agent performed better than the benchmark controller on both metrics for all road types apart from type D. The observation that the trained agent was able to handle road-like excitations better than the benchmark controller was also backed by the tests with the road replay excitations, depicted in Figure 14c. Figure 14: Normalized performance metrics of the trained controller as pareto plots on (**a**) sine sweep, (**b**) synchronous synthetic road excitations, (**c**) real-road replays, and (**d**) asynchronous synthetic road excitations.