# Improved JPS Path Optimization for Mobile Robots Based on Angle-Propagation Theta* Algorithm
## 5 Simulation
### Algorithm Comparison Experiment  
This experiment uses the AP-JPS algorithm, A* algorithm, RRT algorithm, JPS algorithm and AP-Theta* algorithm to conduct comparative experiments in terms of algorithm running time, algorithm memory usage, path length and total path turning angle using maps of downtown Shanghai, downtown New York and downtown Boston extracted from public datasets. The experiments were conducted. The experimental procedure is shown in Figure 13. The comparative results are shown in Table 2. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{1}{c}{\multirow{2}{*}{**Name**}} & \multirow{2}{*}{**Running Time (s)**} & \multirow{2}{*}{**Memory Usage (kb)**} & \multirow{2}{*}{**Path Length (m)**} & \multicolumn{2}{c}{**Total Turning Angle of the**} \\  & & & & & Path (\({}^{\circ}\)) \\ \hline \multirow{4}{*}{Shanghai} & A* & 28.3386 & 2488.4063 & 345.0437 & 2160 \\  & RRT & 99.5774 & 536.7510 & 472.1204 & 4205.3070 \\  & IPS & 0.1217 & 1067.0938 & 345.0437 & 405 \\  & AP-Theta* & 29.0491 & 2740.0223 & 349.2478 & 154.3191 \\  & AP-JPS & 0.2265 & 1224.1230 & 328.8865 & 94.3191 \\ \hline \multirow{4}{*}{New York} & A* & 19.4580 & 2410.4219 & 346.2153 & 2430 \\  & RRT & 104.9274 & 547.0497 & 464.1386 & 4004.6040 \\  & IPS & 0.1659 & 1112.578 & 346.2153 & 1125 \\  & AP-Theta* & 21.4166 & 2715.2300 & 334.7146 & 172.4967 \\  & AP-LPS & 0.289 & 1363.1309 & 334.7146 & 172.4967 \\ \hline \multirow{4}{*}{Boston} & A* & 11.7563 & 1990.7422 & 294.8600 & 1305 \\  & RRT & 61.5348 & 533.3369 & 415.6851 & 2904.0880 \\ \cline{1-1}  & IPS & 0.1074 & 1056.6250 & 294.8600 & 1125 \\ \cline{1-1}  & AP-Theta* & 13.2568 & 2275.0470 & 290.1114 & 464.5372 \\ \cline{1-1}  & AP-JPS & 0.1864 & 1280.2889 & 290.1114 & 464.5372 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Map information selected for the dataset. Figure 13: Experimental procedure of algorithm comparison. (**a**) Shanghai, (**b**) Shanghai, (**c**) New York, (**d**) New York, (**e**) Boston, (**f**) Boston. The following information can be derived from Table 2. From the experiments of the three maps, the AP-JPS algorithm has the smallest total path turning angle and the best path smoothness, and the RRT algorithm has the largest total path turning angle and the worst path smoothness. Among them, the AP-JPS algorithm is effective in reducing the total path turning angle by 58.71% to 84.67% compared with the original JPS. From the resultant path length of each algorithm, the AP-JPS algorithm has the shortest path length and the RRT algorithm has the longest path length, where the resultant path length of the AP-JPS algorithm is 1.61% to 4.68% less than the resultant path length of the original JPS algorithm. Analyzing the space complexity of these algorithms, it can be seen that the RRT algorithm has the lowest memory footprint and the AP-Theta* algorithm has the highest memory footprint. The AP-JPS algorithm has an increased memory footprint compared to the JPS algorithm and a reduced memory footprint compared to the AP-Theta* algorithm. The memory footprint of the AP-JPS algorithm increased by 14.71% to 22.66% and decreased by 43.72% to 55.32% over the memory footprint of the JPS algorithm and the AP-Theta* algorithm. Finally, from the running time point of view, we can find that the JPS algorithm has the shortest computation time and the RRT algorithm has the longest computation time. The computation time of the AP-JPS algorithm is increased compared to the JPS algorithm, and the computation time of the AP-JPS algorithm is increased from 73.35% to 86.01% compared to JPS. However, at the same time, the AP-JPS algorithm has a significant decrease in computing time compared to the AP-Theta* algorithm. The AP-JPS algorithm reduces the running time by 98.59% to 99.22% compared to the AP-Theta* algorithm. The following conclusions can be seen from the results of this comparison experiment.