# A Full-Coverage Path-Planning Algorithm for a Glass-Curtain-Wall-Cleaning Robot Driven by Ropes
## 1 Introduction  
At present, with the rapid development of the social economy and the improvement in people's living standards, the application of glass curtain walls in buildings is becoming increasingly popular [1; 2; 3]. These glass walls need to be regularly cleaned to prolong building service life [4; 5; 6]. While the traditional method for glass curtain wall cleaning relies on manual labor, working at heights poses risks to worker safety. Thus, facade-cleaning robots have been adopted as an assistant or substitute for human workers performing these tasks. In addition, the curved surfaces and irregularly shaped obstacles on buildings place stricter demands on robot performance. For robots working on glass curtain walls, most research has focused on prototype design and stability control; little attention has been paid to the obstacle-overcoming and path-planning abilities of these robots [7; 8; 9]. Therefore, studies on robot DOF extensions and global path-planning algorithms are required. Currently, some robots use wheels or mechanical legs to crawl on facades for wall cleaning [10; 11; 12]. For example, [PERSON] et al. developed a wheeled wall-climbing robot with the ability to climb walls using circular arrays of miniature spines located around the wheel [13]. [PERSON] et al. proposed a flexible and adjustable wheel-leg composite cleaning robot composed of three leg frames on a rotating shaft to expand the movement space [14]. In addition, one type of wall-cleaning robot is driven by ropes. TITO, ROPE RIDE, Sky Scraper-I, etc., have been proposed as robots with a structure combining ropes and sliderails to realize two-DOF motion, but their stability is insufficient on high buildings [15; 16; 17]. To safely apply robots at high altitude, Kite uses four independent winches to control four ropes from four different angles [18]. The winches and cleaning body form a planar two-DOF redundant parallel mechanism, which limits excess body movement, so movement stability can be effectively guaranteed. However, this robot cannot work on a wall with raised obstacles and sunken surfaces because of the lack of movement freedom perpendicular to the wall direction. For the obstacle-overcoming problem, [PERSON] et al. added an electric push rod that can retract perpendicular to the wall for pushing ropes away from the surface [19]. So, the robot can overcome obstacles, but the performance is restricted by the rod length. As taller buildings require more water and cleaning products, this considerably increases the engineering requirements for robot load capacity. However, a robot using legs or wheels is driven by its own adsorption force to move the load, which limits the load capacity; therefore, a rope-driven robot with a high load capacity is more appropriate for window cleaning. From the analysis of complex curtain wall shapes, three-dimensional space motion ability is necessary for a robot to successfully overcome obstacles. Wall modeling is the premise of robot path planning. A variety of environmental modeling methods have been proposed, among which the most common are the grid, topology, and viewable methods [20; 21; 22]. In the grid method, each grid corresponds to a region in the map and represents the environmental information of the region [23; 24; 25]. With the topological method, a region is divided into multiple subspaces according to the geometric features of the environment [26; 27; 28]. The main idea of the viewable method is to view the robot as a particle and the obstacle as a polygon [29; 30; 31]. However, when topological methods encounter regions with similar features, constructing the corresponding topological maps is challenging due to an inability to distinguish similar regions. The disadvantage of the viewable method is that as the number of obstacles increases, the number of lines between vertices increases, which leads to increases in the path-planning complexity and time consumption. Therefore, the topology and viewable methods are unsuitable for wall surfaces with complex-shaped obstacles.