# Reinforcement Learning for Semi-Active Vertical Dynamics Control with Real-World Tests
## 6 Real-World Test
### Results from the Four-Post Test Rig  
The final experiments on the four-post test rig, which was also used to obtain measurement data (cf. Figure 1), were conducted to quantitatively evaluate the trained controller. To set the performance of the RL-based controller into perspective, the offline-optimized benchmark controller described in Section 5.3 was also evaluated on the same excitations. The evaluation of the controllers on the four-post test rig provided several advantages: First of all, every excitation could exactly be repeated for every controller. Quantitatively evaluating different controllers on real roads requires a high accuracy for each repetition. Even small lateral displacements between two experiments might result in altered vertical excitation, e.g., if in one experiment the wheel hits a pothole and misses it in the next pass. The second advantage of the test rig was the additional sensor setup. Force sensors inside the posts could directly measure the wheel load, and high-quality acceleration sensors were additionally used to obtain the chassis acceleration. Measuring the wheel load in real-world driving tests requires additional modification of the vehicle and, thus, was not feasible. To enable a holistic analysis of the vehicle dynamics, all the quantities listed in Table 1 were measured for different vertical excitations. We used a wide range of excitation types to evaluate the performance of the controllers. The first excitation category was sine sweeps ranging from 1 Hz to 30 Hz with exponentially increasing frequency and different constant post zero-crossing velocities of (50, 100, 150, 200, and 250) mm/s. The second type of excitations were synthetic road excitations of type A up to type D according to ISO 8608 [19]. Type A roads represent the smoothest roads and type D represents the bumpiest ones. The work presented in [45] concluded that type A and B roads typically represent roads such as motorways or other  
Figure 13: Real-world test drive on a bumpy road. high-quality roads. Roads of Type D and worse are often used to represent unpaved roads for which a maximum velocity of \(<15\) km/h is recommended [45]. We created the synthetic road excitations such that the vehicle started with a virtual velocity of 1 m/s and increased the velocity linearly up to a maximum velocity. Afterwards, we then decreased the velocity again down to 1 m/s. Additionally, two different versions of the synthetic road were tested: In the first version, all posts were excited with the same excitation, i.e., a synchronous excitation. For the second version, which excited the posts in an asynchronous fashion, the phase between the posts was randomly shifted. The last set of excitations are real-road excitations, which were recorded and reproduced on the testbench and represented both a rough road and a rough bump. From the obtained measurement data, we calculated the road-holding criterion (cf. Equation (15)) and a comfort criterion inspired by ISO 2631-1 [43]. The norm ISO 2631-1 defines comfort metrics for humans, which are subject to whole-body vibrations. To calculate the vertical excitation comfort metric according to ISO 2631-1, the seat surface acceleration first had to be modified by specified filters. Afterwards, the RMS of this filtered acceleration was calculated. Since, in our test setup, the vertical acceleration of the seat surface was not measured, we calculated the filtered RMS for each of the three chassis accelerations and took the mean value for evaluation. After calculating the comfort and road-holding criterion for both the RL-based and the benchmark controller, a reference value was calculated by normalizing the metrics of the RL-based controller to the metrics of the benchmark controller. This resulted in a metric that was easy to interpret: Values below 1 indicated that the RL-based controller performed better on this metric, and vice versa.