# Laser Ablation Manipulator Coverage Path Planning Method Based on an Improved Ant Colony Algorithm
## 2 Point Cloud Pre-Processing  
### Point Cloud Denoising and Simplification  
The point cloud is a dataset of points that have been used widely to represent shapes since the pioneering work of [PERSON] et al. [28]. The main focus of this study was on the application of the point cloud in path planning. Using the point cloud has several advantages. First, the point cloud data are easy to acquire--one scanner is sufficient. Moreover, the point cloud is suitable for complex geometries. Furthermore, it does not require global maintenance of the topology. The advantages of point-cloud-based methods over mesh-based methods are apparent when the workpiece is highly \begin{table}
\begin{tabular}{c c c} \hline \hline
**Section** & **Content** & **Function** \\ \hline
1 & Introduction & \\
2 & Point Cloud Pre-Processing & Get path points from the point cloud data, \\  & & finish the inverse kinematics \\
3 & Optimisation Objective & Establish a path evaluation model \\
4 & Improved Ant Colony Algorithm & Solve the CPP problem with the improved \\
5 & Method and Simulation & Summary and verification \\
6 & Conclusions and Further Studies \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Contents and functions of each section. freeform and complex [28]. Finally, using a point cloud can skip the surface fitting process to generate the tool path directly, which is the idea of direct machining [29]. However, the use of the point cloud also has disadvantages. To improve the accuracy of the representation, the density of the point cloud data should typically be enormous. This increases the complexity of path planning. Therefore, before path planning, the point cloud data need to be processed to extract the required path points. The problem of path planning using the point cloud has been investigated in many studies. [PERSON] et al. [30] demonstrated a point-cloud-based tool path generation algorithm using different tool path patterns previously designed. This method can reduce the path-planning complexity but limits the application of the method in complex geometries. [PERSON] et al. [31] proposed a method for planning an isoparametric tool path from a point cloud and employed a point-based conformal map to build the parameterisation. However, the uneven spatial path reduces its efficiency. [PERSON] et al. [32] developed an algorithm to generate tool paths for direct machining, including dividing the surface into ranges and generating B-spline curves within each range. However, the program is not equipped to handle surfaces with shapes other than a rectangle. [PERSON] et al. [33] proposed a path-planning method based on a discontinuous grid partition algorithm using the point cloud for in situ printing and obtained a good printing effect. However, the influence of each parameter still needs further study. [PERSON] et al. [34] proposed a method for point cloud simplification, denoising, and boundary extraction based on a k-neighbourhood octree structure and applied it in grinding path planning. In addition to the personalised methods described above, one common method is the point cloud slicing technique [35; 36]. This method cuts the workpiece point cloud model through a series of parallel planes. Then, the adjacent points of the workpiece point cloud data near the two sides of each slice are matched to obtain the intersections between the matching points and slices. After each intersection is moved a certain distance along its normal vector, the processing path is obtained by connecting each point end to end. However, this method does not consider the path-planning problem as an optimisation problem. The path obtained is feasible but not optimal. Moreover, key parameters, such as cutting distance and direction, require artificial input, adding artificial factors to a certain extent. Herein, a novel method is proposed for point cloud simplification based on a continuous grid partition.