# Improved JPS Path Optimization for Mobile Robots Based on Angle-Propagation Theta* Algorithm
## 5 Simulation
### Data Set Map Experiment  
The experiments were conducted using a public dataset freely distributed by Moving AI Lab. Four sets of maps of 80 \(\times\) 80, 512 \(\times\) 512, and 768 \(\times\) 768 sizes are used for the dataset maps. The specific map information is shown in Table 3.  
In this experiment, A*, JPS, AP-JPS and AP-JPS after polynomial optimization are selected for experimental comparison. The experimental data and results are the average of ten experiments, and the results are shown in Figure 14.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Number** & **Map Name** & **Map Size (m)** & **Number of Obstacles** & **Max Length** \\  & & & & **Problem in Scenario** \\ \hline  
ividendThe generated path lengths, total path turning angles, and actual data of the three algorithms were recorded in the twelve sets of experiments as shown in Tables 4-6. Figure 14: Data set experiment. (**a**) AR0310 SR, (**b**) AR0513 SR, (**c**) AR0709 SR, (**d**) AR0709 SR, (**e**) divideandconquer, (**f**) plunderisle, (**g**) moonglade, (**h**) harvestnoon, (**i**) BlastFurnace, (**j**) Crossroads, (**k**) Hellfire, (**l**) Sapphirelsles. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{1}{c}{**Number**} & \multicolumn{1}{c}{**Map Name**} & \multicolumn{1}{c}{**Algorithm Type**} & \multicolumn{1}{c}{**Path Length (m)**} & \multicolumn{1}{c}{**Total Turning angle**} & \multicolumn{1}{c}{**Operation Time (s)**} \\ \hline
1 & & A* & 1175.8 & 4140 & 793.3247 \\
2 & Crossroads & JPS & 1175.8 & 2385 & 8.4912 \\
3 & & AP-JPS & 1151.4 & 412.6626 & 15.9326 \\ \hline
4 & & A* & 1136.5 & 4200 & 781.1085 \\
5 & BlastFurrace & JPS & 1136.5 & 1665 & 9.5450 \\
6 & & AP-JPS & 1097.0 & 359.3899 & 16.5546 \\ \hline
7 & & A* & 980.7048 & 1039 & 717.4127 \\
8 & Hellfire & JPS & 980.7048 & 675 & 15.4673 \\
9 & & AP-JPS & 948.6092 & 144.3275 & 24.5147 \\ \hline
10 & & A* & 884.8154 & 3690 & 561.7834 \\
11 & Sapphirelsles & JPS & 884.8154 & 1165 & 12.2100 \\
12 & & AP-JPS & 851.2148 & 419.2467 & 21.2617 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The \(768\times 768\) grid map experiment. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{1}{c}{**Number**} & \multicolumn{1}{c}{**Map Name**} & \multicolumn{1}{c}{**Algorithm Type**} & \multicolumn{1}{c}{**Path Length (m)**} & \multicolumn{1}{c}{**Total Turning Angle**} & \multicolumn{1}{c}{**Operation Time (s)**} \\ \hline
1 & & A* & 68.0122 & 315 & 0.1654 \\
2 & AR0513 SR & JPS & 68.0122 & 315 & 0.0397 \\
3 & & AP-JPS & 64.3672 & 39.5076 & 0.0751 \\ \hline
4 & & A* & 74.7696 & 495 & 0.2241 \\
5 & AR0709 SR & JPS & 74.7696 & 225 & 0.0248 \\
6 & & AP-JPS & 71.4807 & 104.1320 & 0.0643 \\ \hline
7 & & A* & 57.6233 & 585 & 0.1523 \\
8 & AR0310 SR & JPS & 57.6233 & 225 & 0.0137 \\
9 & & AP-JPS & 54.3827 & 94.3987 & 0.0674 \\ \hline
10 & & A* & 78.0833 & 990 & 0.2057 \\
11 & AR0704 SR & JPS & 78.0833 & 675 & 0.0303 \\
12 & & AP-JPS & 77.6401 & 378.6445 & 0.0988 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The \(80\times 80\) grid map experiment. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{1}{c}{**Number**} & \multicolumn{1}{c}{**Map Name**} & \multicolumn{1}{c}{**Algorithm Type**} & \multicolumn{1}{c}{**Path Length (m)**} & \multicolumn{1}{c}{**Total Turning Angle**} & \multicolumn{1}{c}{**Operation Time (s)**} \\ \hline
1 & & A* & 502.7838 & 2690 & 93.6902 \\
2 & divideandconquer & JPS & 527.5706 & 1035 & 3.9906 \\
3 & & AP-JPS & 500.2249 & 291.3104 & 7.9424 \\ \hline
4 & & A* & 519.9554 & 891 & 100.7357 \\
5 & plunderisle & JPS & 519.9554 & 765 & 3.8260 \\
6 & & AP-JPS & 492.9167 & 80.2559 & 5.9129 \\ \hline
7 & & A* & 516.2641 & 2430 & 90.5687 \\
8 & harvestmoon & JPS & 516.2641 & 855 & 4.0340 \\
9 & & AP-JPS & 503.5609 & 182.1982 & 5.9667 \\ \hline
10 & & A* & 589.3209 & 2745 & 90.1968 \\
11 & moonglade & JPS & 589.3209 & 1035 & 4.6622 \\
12 & & AP-JPS & 570.7837 & 288.7079 & 7.1101 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The \(512\times 512\) grid map experiment.