## 2 Structural Design of Photovoltaic Panel Cleaning Robot
### Upper Structure  
In general, the composition of the upper structure comprised three parts, i.e., the upper rotating structure, the arm frame structure, and the cleaning device. The engine, load sensitive pump, multi-way valve group, electric control cabinet, fuel tank, etc., were installed in the upper turning structure of the vehicle to achieve the hydraulic drive of the entire vehicle. The triangular design of the boom structure was adopted to make the structure stable and ensure the stability of the cleaning device during operation. Three cylinders were used to drive the boom mechanism to rotate, and sensors were used to realize closed-loop control to improve the accuracy of control. The cleaning device was designed as a rolling brush structure which realizes the cleaning of dust particles on the smooth surface under the drive of the cleaning motor without hydration operation; in addition, this design reduces the cost of the device. All structures were connected and fixed by pins and bolts to ensure that the upper structure can meet the requirements of photovoltaic panel cleaning in harsh environments. As shown in Figure 10.  
The cleaning device was designed with two sides of the scraper, and the brush was driven by the hydraulic motor to clean the dust particles on the photovoltaic panel surface. Both sides of the scraper can not only remove the dust particles on the plate surface, but also avoid the secondary pollution of the plate surface before and after cleaning. Figure 10: Upper robot structure. In the design, it is necessary to study the mapping relationship between the hydraulic actuators of the boom and the joint angle and establish the coordinate system shown in Figure 11.  
According to the coordinate system built by the above diagram, the mapping relationship between the displacement variation of the big arm, the small arm and the sweeper cylinder and the joint angle can be solved by geometric transformation, and the relationship is as follows:  
\[\left\{ \begin{array}{l}L_{AB}=\sqrt{L_{AC}^{2}+L_{BC}^{2}-2\cos(180^{{}^{ \circ}}-\angle BCD-\theta_{2})L_{AC}L_{BC}}\\ \theta_{2}=180^{{}^{\circ}}-\angle BCD-ar\cos(\frac{L_{AC}^{2}+L_{BC}^{2}-L_{ AB}^{2}}{2L_{AC}L_{BC}})\end{array} \right., \tag{8}\]  
\[\left\{ \begin{array}{l}L_{EF}=\sqrt{L_{ED}^{2}+L_{DF}^{2}-2\cos(180^{{}^{ \circ}}-\angle EDH-\theta_{3})L_{ED}L_{DF}}\\ \theta_{3}=180^{{}^{\circ}}-\angle EDH-ar\cos(\frac{L_{ED}^{2}+L_{DF}^{2}-L_{ EE}^{2}}{2L_{ED}L_{DF}})\end{array} \right., \tag{9}\]  
\[\left\{ \begin{array}{l}L_{KG}=\sqrt{L_{KH}^{2}+L_{HG}^{2}-2\cos(180^{{}^{ \circ}}+\angle KHN-\angle GHD+\theta_{4})L_{KH}L_{HG}}\\ \theta_{4}=180^{{}^{\circ}}+\angle KHM-\angle GHD-ar\cos(\frac{L_{KH}^{2}+L_{ BC}^{2}-L_{KG}^{2}}{2L_{KH}L_{HG}})\end{array} \right., \tag{10}\]  
where \(L_{AB}\), \(L_{EF}\) and \(L_{KG}\) denote the displacement changes in the big arm cylinder, the small arm cylinder, and the sweeper cylinder, respectively; \(\theta_{1}\), \(\theta_{2}\) and \(\theta_{3}\) represent the angle between the big arm and the upper frame, the angle between the small arm and the big arm, and the angle between the sweeping plates, respectively. Combined with the established coordinate system and the angle variables of the boom mechanism, the Monte Carlo algorithm was used to solve the end trajectory space of the robot. The end space formed is described below. As depicted in Figure 12, it can be seen that the end working space of the photovoltaic panel cleaning robot is similar to a hemispherical body; from the \(Y\)-\(Z\) working plane, it can be seen that the limit position that can be reached during forward and reverse cleaning is \([-2.85\) m, \(2.85\) m]; combined with the cleaning radius requirements of the photovoltaic panels, the effectiveness of the designed boom cleaning device was verified. Figure 11: Coordinate system of the arm of the photovoltaic cleaning robot.