## 1 Introduction
The former requires guide rails permanently fixed on the PV panel arrays for horizontal motion [18; 19]; otherwise, it runs on the edge of PV module arrays [20; 21; 22; 23; 24], namely module-mounted robotics. Consequently, this particular type of PV cleaning robot is typically well-suited for large-scale PV plants characterized by the continuous straight alignment of PV panels. The latter features a structural design similar to that of a mobile robot equipped with a suction cup [25], wheels [26; 27; 28], or belt-based tracks [29; 30; 31] to facilitate its movement. These are commonly employed for utility-scale PV plants where the adjacent PV panels might exhibit uneven planes, edge misalignment, or large gaps. The commercial PV cleaning robot [25], utilizing suction cups to adhere to PV panels, can achieve a maximum efficiency of 1040 m\({}^{2}\) per hour, even on steep rooftops with inclinations of up to 45\({}^{\circ}\). While PV cleaning mobile robots equipped with wheels are susceptible to disturbances caused by gaps between two adjacent PV panels and the PV array mounting brackets, those utilizing belt-based tracks, similar to tanks, are not affected [28]; in particular, some research indicates how to design the tank suspension in the PV cleaning mobile robots to decrease the impact on the PV panels [13; 32]. Moreover, the commercial PV cleaning robot equipped with a belt-based track system [30] has the capability to achieve a maximum cleaning efficiency of up to 1600 m\({}^{2}\) per hour, positioning it as a highly promising cleaning solution for distributed PV plants. However, this specific PV cleaning robot still faces challenges in terms of slipping and falling, threatening robot safety when operating on wet tilted PV surfaces. Slip resistance has been recognized as the key feature of the belt-based track, aiming to enhance the anti-slippage capability of this specific PV cleaning robot. Although numerous studies ([33; 34; 35; 36] and references therein) have investigated the effects of rubber soling materials on floor surfaces, there has been limited research, except for our earlier study [37; 38], regarding suitable material coatings for the belt-based track that can provide sufficient grip for the PV cleaning robot during the removal of dust from wet PV panels. It was observed that shore hardness and surface roughness significantly impact the slip resistance of rubber soles in both dry and wet flooring conditions [33]. The coefficient of friction (COF) for rubber soles with a hardness of A65 is 0.95 in dry flooring conditions, while for rubber soles with a shore hardness above 85, it is 0.50. In wet condition tests, the COF for rubber soles with a hardness of A65 is 0.88. However, the use of different types of slipmeters can result in varying friction indices on uniform surface roughness [34]. To tackle the aforementioned issues, extended from our previous study [38], this paper investigates the geometric and hardness parameters of tank track grooves equipped on PV cleaning robots via the novel slip resistance test apparatus. The proposed apparatus simulates both dry and wet working conditions ofn PV panels during dust removal by utilizing water sprayer nozzles supplied with controlled water flow. The tilt angle of PV panels is continuously adjusted through a hinged lever mechanism while simultaneously measuring the \(x\)-axis component of gravity force. Experiments are conducted to determine the relationship between the coefficient of static friction (COSF) and factors such as shore hardness, contact area, and outside pattern. Referring to the relationship between these factors with respect to COSF, the suggested intrinsic parameters can be obtained to design the belt-based track for PV cleaning robots, with the aim of ensuring safety during the cleaning of tilt PV panels. Apart from our earlier study and the existing literature, the main contributions of this paper can be summarized as follows:  
1.