# Path Planning of Rail-Mounted Logistics Robots Based on the Improved Dijkstra Algorithm
## 3 Results and Discussion
### Dynamic Test Experiment  
In order to verify the feasibility of the aforementioned path-planning algorithm, Matlab is used to verify the algorithm combined with an example. Figure 8 shows the simulation diagram of the running environment of the rail-mounted robot. The workshop map layout is created using the raster method. Among them, the white grid represents the track, which is a passable path. The black grid represents the impassable path. The orange grid represents the material station in the workshop. The grid number represents the workstation number. The mode of operation of the robot in orbit is a two-way single lane.  
\begin{table}
\begin{tabular}{c c c c} \hline \multirow{2}{*}{**Serial Number**} & \multicolumn{2}{c}{**The Mean Coordinates**} & \multirow{2}{*}{**Actual Coordinates (m)**} & \multirow{2}{*}{**Error (m)**} \\  & **of the UWB** & & & \\  & **Measurements (m)** & & & \\ \hline
1 & (101.22, 101.22) & (101.10, 101.10) & (0.12, 0.12) \\
2 & (100.31, 131.64) & (100.01, 131.48) & (0.03, 0.16) \\
3  
At one time, there were three machines on the track moving to three different target nodes. Figure 9a shows the path initially planned by the traditional Dijkstra algorithm, and Figure 9b shows the path dynamically adjusted by the improved Dijkstra algorithm. In the figures, the three lines with different colors represent the planned paths of the three robots, respectively. A triangle represents the starting point, and a circle represents the ending point. The line colors are blue, red, and green in order of robot priority from highest to lowest. Figure 9c,d show the spatio-temporal graphs of the planned path before and after dynamic adjustment, respectively. Table 5 shows relevant parameters before and after dynamic adjustment.  
Comparing Figure 9a with Figure 9b, it can be observed that the blue robot with the highest priority during the initial path planning did not change the planned trajectory after the dynamic adjustment, whereas the red robot and the green robot made dynamic adjustments. Since the blue robot traveled according to the established route, its traveling time did not change. Comparing Figure 9c with Figure 9d, it can be observed that in order to prevent an on-orbit collision, the running time of the red robot and green robot increased by 30 s and 40 s, respectively, but the on-orbit collision and congestion problems of the robots are avoided.  
Figure 8: Grid diagram of robot operating environment.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \begin{tabular}{c} **Robots** \\ **Serial** \\ **Number** \\ \end{tabular} & \begin{tabular}{c} **Priority** \\ **Site** \\ \end{tabular} & \begin{tabular}{c} **Initial** \\ **Site** \\ \end{tabular} & \begin{tabular}{c} **Target** \\ **Site** \\ \end{tabular} & \
\begin{tabular}{c} **The Planned Path** \\ **before the Dynamic** \\ **Adjustment** \\ \end{tabular} &
\begin{tabular}{c} **The Planned Path** \\ **after the Dynamic** \\ **Adjustment** \\ \end{tabular} \\ \hline Blue \(r_{1}\) & \(\mathrm{P_{1}}\) & 116 & 231 & 77-76-206-204-243 & 77-76-206-204-243 \\ Red \(r_{2}\) & \(\mathrm{P_{2}}\) & 168 & 236 & 233-27 & 233-206-204-74-76-27 \\ Green \(r_{3}\) & \(\mathrm{P_{3}}\) & 274 & 102 & 149-134 & 149-214-200-135-134 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Relevant parameters before and after dynamic adjustment.