# Path Planning of Rail-Mounted Logistics Robots Based on the Improved Dijkstra Algorithm
## 3 Results and Discussion
### Formatting of Mathematical Components  
The following considers the on-orbit collision of two robots as an example to conduct a simulation test and analysis. Table 6 shows the relevant parameter settings for the on-orbit operation of the robots.  
Based on the task parameters listed in Table 6, Figure 10a shows the initial path planned by the distribution system for robots \(r_{5}\) and \(r_{6}\). In Figure 10a, the initially planned paths of robot \(r_{5}\) and robot \(r_{6}\) overlap between sections 76-141-168 of the station, resulting in an on-orbit collision between the two robots. Since robot \(r_{5}\) has a higher priority than robot \(r_{6}\), the path of the robots needs to be adjusted. The time taken and distance traveled by robot \(r_{6}\) are calculated to take delay waiting and replanning respectively, and the results are shown in Table 7.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Robots** & **Priority** & **Initial** & **Target** & **The Planned Path before the Dynamic** \\
**Serial Number** & **Site** & **Site** & **Adjustment** \\ \hline \(r_{5}\) & P\({}_{1}\) & 222 & 51 & 222-141-76-80-51 \\ \(r_{6}\) & P\({}_{2}\) & 12 & 168 & 12-11-76-168 \\ \hline \hline \end{tabular}
\end{table}
Table 6: The relevant parameter settings for the on-orbit operation of the robots.  
Figure 9: (**a**) The path initially planned by the traditional Dijkstra algorithm. (**b**) The path is dynamically adjusted by the improved Dijkstra algorithm. (**c**) The spatio-temporal graph of the planned path before the dynamic adjustment. (**d**) The spatio-temporal graph of the planned path after the dynamic adjustment. Three lines with different colors represent the planned paths of the three robots, respectively.  
* Delay waiting: As shown in Table 7, if the robot chooses to wait for a delay at station 60 before a conflict occurs, the robot can continue to pass when it passes through station 76. When the delay waiting strategy is adopted, the total traveling time of the robot is 221.4 s, the waiting time is 75.7 s, and the traveling distance remains unchanged. After the robot adopts the delay waiting strategy, the time of executing the distribution task increases by 48.62%, and the driving path does not change.
* Replanning: As shown in Table 7, after the replanning strategy is adopted, the robot's traveling time is 197.1 s and its traveling distance is 150 m. After replanning, the delivery time and driving distance increase by 25.59% and 14.28%, respectively. Therefore, adopting the replanning strategy to solve the conflict between two robots can improve the efficiency of distribution.  
To sum up, in this case, when the robots encounter conflict in opposite directions, the replanning strategy takes 14.28% longer driving distance than the delayed waiting strategy, but the replanning strategy takes 17.82% less time than the delayed waiting strategy. Therefore, the replanning strategy was chosen to improve the efficiency of material distribution. After replanning, the driving paths of the two robots are shown in Figure 10b.