# A Framework for Coverage Path Planning Optimization Based on Point Cloud for Structural Inspection
## 1 Introduction  
Over the last few years, different practical applications emerged requiring periodic inspections to verify possible structural changes, guaranteeing safety through preventive assessment. For instance, large structures, such as dams and slopes, need constant monitoring, and due to the size of these structures, manual inspections are time-consuming and may present risks to humans. In this context, Unmanned Aerial Vehicles (UAVs) arose as a prominent solution to automate this process in a cost-effectively way. In addition, UAVs have positioned at the forefront of different application fields, such as infrastructure inspection [1, 2], search and rescue [3, 4], delivery [5, 6], among others. In the scenario of large structures' inspections, the UAV may help decrease the mission's complexity, such as data gathering and geometry land specifications due to its maneuvering flexibility, high versatility, and the possibility of attaching new technologies into it [2]. Inspections on large structures with UAVs should minimize flight time due to battery time restrictions and identify the terrain's topographic features. In this sense, Coverage Path Planning (CPP) aims at finding the best path to coverage of a determined area respecting the operation's restrictions [7]. Thus, the development of several algorithms allowed the application in these kinds of processes [8, 9, 10]. For example, there are several applications, such as underwater inspection [11] and aerospace [12] tasks. Note that the accurate 3D models are the desired result for inspections. However, some issues remain unsolved from a computational geometry perspective. Path planning refers to finding an optimal route of a moving object from an initial to a final point [13]. Several works have been proposed in the last few years to improve this technique and apply it in the robotics context. In [14], the authors developed a cell decomposition algorithm for robotswith contact sensors for covering unknown environments in an online manner. The work of [15] proposed a hybrid methodology for mobile robots on an autonomous mission involving an offline approach that uses the Direct-DRRT* algorithm and the Artificial Potential Fields (APF) algorithm for the online planner. In [16], the authors used a bat algorithm for solving the mobile robots' global localization problem. Robots need to perceive the world to work in unstructured environments. In this sense, with the advent of low-cost 3D sensing hardware and in cloud processing, 3D perception in robotics has gained more attraction [17]. Therefore, dense point cloud generation has faced a great advance in the last few years thanks to the rapid development of technologies and algorithms. For instance, [PERSON]. [18] developed an improved delineation method using high-density LiDAR. In [19], the authors worked with image-based 3D reconstruction. They presented a quantitative comparison of several multi-view stereo reconstruction algorithms. The work of [20] proposed an optimization-based algorithm for planar patches extraction from noisy point-cloud data. 3D objects can provide information for creating routes or even for refining previously created paths. It is possible to determine many properties of 3D data objects. However, point cloud data are very unorganized, noisy, and sparse, demanding processing stages to use this information [21]. In addition, in some situations, the foreground is very mixed with the background due to sensor limitations to precisely acquire 3D data. In this sense, point cloud learning has increasing attention with applications in many domains, such as computer vision, autonomous driving, and robotics. The representation of 3D data is generally in different formats, including depth images, point clouds, and meshes. As a commonly used format, point cloud representation preserves the original geometric information in 3D space, representing the environment without discretization [21].