# Laser Ablation Manipulator Coverage Path Planning Method Based on an Improved Ant Colony Algorithm
## 6 Conclusions and Further Studies  
The coverage path generation in a complex free-form surface is a representative problem that has been steadily investigated in path planning and automatic control. Most methods, including the point cloud slicing method, use regular curves or broken lines to traverse the fixed area. The drawback is that they need to be improved in terms of efficiency and effect.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Point Cloud Slicing** & **Proposed CPP Method** & **\%Age Improvements** \\ \hline Path length (mm) & 3972 & 2063 & 48.06\% \\ Optimisation value & 2917.13 & 920.85 & 68.43\% \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison of the two methods.  
Figure 10: Effect of laser cleaning: (**a**) workpiece before cleaning, (**b**) workpiece after cleaning, and (**c**) workpiece during cleaning.  
To overcome these issues, the path-planning method was divided into three parts: environmental modelling, optimisation objectives and boundary conditions, and optimisation methods. New methods were used in each part.  
(1) Laser processing is characterised by a variable laser spot size. A new point cloud processing algorithm was proposed for environmental modelling, which can work well with this characteristic.  
(2) For optimisation objectives, a novel path evaluation model was established by introducing the trajectory optimisation information. For different task objects and task demands, more types of path shape can be obtained by adjusting the weight coefficients' concrete value and normalisation coefficients.  
(3) An improved ant colony algorithm was proposed to solve the CPP problem. Based on the max-min ant system, two improvement measures were proposed. One was a method of calculating the transition probability based on randomness. The other was the addition of a relative factor in the process of pheromone updating. The numerical studies indicated that the improvement measures improved the global search ability of the algorithm, and the improved ant colony algorithm obtained better performance than that of ACO and MMAS.  
Combining all three parts, a new CPP method was proposed based on point cloud data. The test results revealed that the method generated a more efficient path than the point cloud slicing technology that is currently commonly used. Thus, the proposed method provides a useful reference for the path planning of manipulators on complex free-form surfaces. However, due to the heuristic algorithm's randomness, the global optimal solution cannot be obtained each time. Besides, some of the optimisation target parameters also need to be modified after experimental verification, which increases the complexity of using the proposed method for different tasks. More-effective metaheuristic algorithms and path evaluation models should be considered to achieve much quicker and more-practical coverage path generation in further studies. Moreover, the ant colony algorithm should be combined with the commonly used parallelism framework to improve the algorithm's running speed, thus reducing the proposed method's overall running time.  
Conceptualisation, Y.D. and L.L.; methodology, X.Y. and Y.W.; software, X.Y. and L.L.; supervision, L.H.; writing--original draft, X.Y.; writing--review and editing, L.H. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China, grant number 5187052280, and the Sichuan Action and Innovation Driven Fund Project of \"Made in China 2025\".  
The authors declare no conflict of interest.