# Design and Optimization of Non-Coplanar Orbits for Orbital Photovoltaic Panel Cleaning Robots
###### Abstract
Design and Optimization of Non-Coplanar Orbits for Orbital Photovoltaic Panel Cleaning Robots [PERSON], [PERSON], [PERSON], B. Design and Optimization of Non-Coplanar Orbits for Orbital Photovoltaic Panel Cleaning Robots [PERSON], [PERSON], [PERSON], B. Design and Optimization of Non-Coplanar Orbits for Orbital Photovoltaic Panel Cleaning Robots [PERSON], [PERSON], [PERSON], [PERSON], B. Design and Optimization of Non-Coplanar Orbits for Orbital Photovoltaic Panel Cleaning Robots [PERSON], [PERSON], [PERSON], Y.  
constrained by the terrain and lacks versatility. [PERSON] et al. [7], [PERSON] et al. [8], and Serbot Swiss Innovations [9] advocate for the use of autonomous mobile cleaning robots that can be deployed on solar photovoltaic (SPV) panels to facilitate their cleaning. The disadvantages of this solution include the difficulty the autonomous mobile cleaning robot faces in spanning large distances between PV panels as well as limitations imposed by the tilt angle of the panels. [PERSON] et al. [10] employed a drone to clean PV panels, representing a novel approach. However, it is important to note that the dust stirred up by the drone's rotating blades during operation is likely to settle back onto the surface of the PV panels. This phenomenon can be extremely detrimental to electricity generation from the panels. As a result, various types of orbital cleaning robots have been developed [11; 12; 13; 14; 15]. The robots use the aluminum edges as tracks to facilitate their movement across the photovoltaic panels. The wheel assemblies maintain close contact with the edges of the panels, ensuring that the robots remain stable while on the surface. While they can achieve varying degrees of comprehensive cleaning by spanning linear orbits, they often overlook a critical factor: the installation environment of the PV panels. In fact, PV panels can exhibit highly complex relative positions based on the installation environment. For instance, in a desert setting, the foundation pillars of the PV panels may sink or tilt due to geological factors, leading to uneven relative positions among the panels. Consequently, the trajectory spanning the PV panels is no longer a simple linear path but rather a non-coplanar trajectory in three-dimensional space. Therefore, designing a non-coplanar orbital for robots to achieve efficient cleaning has become an urgent challenge. The non-coplanar orbital serves as a crucial link for the PV panel cleaning robot to operate effectively, and its design concept is realized through the development and modeling of non-coplanar trajectories. In the design of non-coplanar trajectories, various mathematical methods are widely adopted to meet the needs of different application scenarios. Among them, the B-spline curve method [16], the NURBS curve method [17], and the Bezier curve method [18] are some of the primary techniques. For instance, [PERSON] et al. [16] implemented adaptive motion planning for unmanned aerial vehicles (UAVs) using B-spline curves. However, B-spline curves may not accurately represent the desired shape in three-dimensional space, which can lead to potential issues in the design outcomes. [PERSON] et al. [17] employed non-uniform rational B-spline (NURBS) curves for Cartesian trajectory planning in industrial robots, significantly improving robotic motion performance. The fundamental linear decomposition of NURBS curves into 3D line shapes involves the computation of tangents and curvature, resulting in a highly complex decomposition process. Bezier curves, as a kind of spline curve, provide a more concise and controllable solution, which is quite widely used in the study of path planning [18; 19; 20; 21; 22]. In addition, [PERSON] et al. [23] combined aero-assisted orbital maneuvers with hp-adaptive pseudospectral methods to reduce fuel consumption. The application of this advanced approach to non-coplanar orbit design will also enhance the efficiency of cleaning robots.