## 5 Experiment Setup  
The tests were carried out using the SPCR with and without the installation of a multi-suspension unit to evaluate the effectiveness of the proposed design. The SPCR, weighing 90 kg, was equipped with two track-wheeled systems, each having a width of 75 mm, and it was observed that the robot can function adequately with or without the multi-suspension unit. The induced vibration is likely caused by mechanical deviations arising from structural misalignment, machining tolerances, and asymmetrical components during the robot assembly process, as well as certain levels of elasticity and flexibility exhibited by PV panels. It is anticipated that the multi-suspension unit may assist in reducing the deflection of PV panels not only during brush rotation but also during the movement of the entire SPCR. Therefore, it is necessary to individually investigate these situations. To validate the effect of solely brush rotation on PV panel vibration, a configurable PV module, as depicted in Figure 14a, with a single PV panel fixed to the rack at a 10 degrees tilt southward along its short edge, was employed. The SPCR was positioned stationary on the PV module while the brush was rotating to observe the effect on PV panel vibration. Furthermore, the vibration caused by the SPCR during full operation, i.e., while passing over PV arrays with the brush rotating, was evaluated for landscape and portrait PV modules. The former, illustrated in Figure 14b, consists of three PV panels arranged in a single row with their short edges aligned, forming a horizontal profile. The latter configuration, shown in Figure 14c, consists of two PV panels connected in a series along their long edges, introducing a vertical profile. All PV module configurations were constructed in accordance with the standard [22] to replicate practical PV modules, aiming to observe their true behavior. The deflection of PV panels was measured using an instrument, as shown in Figure 15. This instrument consists of a Mitutoyo 543-400B round-type dial gauge (DG) with a resolution of 0.01 mm, which is attached to a magnetic base stand. This configuration allows for easy positioning and orientation of the DG perpendicular to the PV panel surface. Care was taken to ensure that the tip of the DG made contact beneath the backside of the PV panels without scratching the module's back surface. The deflection values were recorded using a computer connected to the DG via a transmission cable. All tests solely focused on the impact of the SPCR being in operation on the vibration of PV panels. Thus, external factors such as windy conditions, earthquakes, or other fluctuations were prevented from influencing the experiments. In addition, the PV panel support frame is designed to be rigid, and its deformation during the experiment is negligible. The speed of the SPCR was controlled to move at approximately 20 m \(\cdot\) min\({}^{-1}\), and it was recognized that the speed of the brushes could significantly affect the vibration. Therefore, the determination of the brushes' rotating speed was based on the Nyquist-Shannon sampling  
Figure 13: The multi-damper unit of PV panel cleaning SPCR. theorem. As a result, the sampling frequency (\(f_{s}\)) of the logged deflection values had to satisfy the following inequality:  
\[f_{s}\geq\frac{\omega}{\pi} \tag{28}\]  
where \(\omega\) is the angular velocity of the brushes. For the angular velocity of brushes \(\omega~{}=~{}6.67\pi~{}\mathrm{rad}\cdot\mathrm{s}^{-1}\), the sampling period is defined as \(t_{s}\triangleq 1/f_{s}\) should be less than 0.15 s. Therefore, the chosen sampling period is 0.1 s.  
To assess the effectiveness of the multi-suspension unit in reducing the vibration amplitude of the PV panel across all experimental data, we introduced a metric called deflection deviation (\(\Delta z\)). This metric quantifies the change in deflection per unit of time.