## 5 Conclusions  
To improve factory operation efficiency, the engineers can determine the path priority for each robot depending on the importance of the robot's task and then request the shorter average path for total robots. In this paper, an efficient navigation algorithm with path priority (NSPP) for multi-robot moving is proposed. Multiple robots can reach their respective target points with highly efficient paths and without collisions in a flat space with obstacles. The methods of ROA and SDA also achieved collision-free navigation for multiple robots, but in this study, we used the path-priority concept, GVD and Dijkstra, and obstacle avoidance strategies to develop an efficient NSPP to achieve the same objective. The performance of the NSPP was compared with those of the SDA and ROA, and it was found that the NSPP has a better average trajectory length than the others in four- or eight-robot configurations, as shown in Figure 16.  
We have to mention that the proposed NSPP can be applied to any number of robots; however, it is not guaranteed that the performance of the proposed NSPP is the best compared to other methods when the number of robots increases or the working environment is changed. We have to admit that the NSPP still needs some improvement such as having a path priority that can be replaced by moving priority, in other words, maybe the robot with higher moving priority can move without avoiding any other lower priority robot; on the contrary, the lower moving priority robot should avoid hitting higher moving priority robot on the way. In other words, the robot with higher moving priority can follow its planned path to move, and the robot with lower moving priority has to change its planned  
Figure 16: (**a**) Trajectory length comparison of ROA, SDA, and NSPP for four robots; (**b**) trajectory length comparison of ROA, SDA, and NSPP for eight robots.  
path frequently or maybe uses speed adjustment to slow down so that the robot with higher moving priority is not hit by the robot with lower moving priority. However, whether moving priority or path priority has a more efficient performance will be studied in the near future.  
At last, we have to mention that there is also a method called \"visibility graph\" [34] for dealing with the path planning problem for a robot. The purpose of the visibility graph is to find the shortest path for a robot, which is similar to the GVD in the proposed method. However, comparing the time complexity between the GVD and the visibility graph, there are O (n log n) for the GVD [35] and O (n\({}^{2}\) log n) for the visibility graph [34], where \(n\) is the total number of input points. Hence, the time cost of using the GVD to find the feasible path is faster than using the visibility graph.  
Conceptualization, S.-K.H. and C.-H.S.; Methodology, S.-K.H. and C.-H.S.; Resources, W.-J.W.; Software, S.-K.H.; Supervision, W.-J.W.; Validation, S.-K.H. and W.-J.W.; Writing--original draft, S.-K.H.; Writing--review and editing, W.-J.W. All authors have read and agreed to the published version of the manuscript.  
This research was funded by Ministry of Science and Technology of Taiwan with the grant number 110-2634-F-008-005.  
Data Availability Statement: Data sharing not applicable.  
The authors declare no conflict of interest.