# Research on Path Planning of Mobile Robot Based on Improved Theta* Algorithm
## 3 Simulation
### Experiment of Comparing W-Theta\({}^{\star}\) Algorithm with Other Algorithms
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Map Type**} & **Map Size/m\({}^{2}\)** & **Map Name** & \
\begin{tabular}{c} **Number of** \\ **Obstacles** \\ \end{tabular} &
\begin{tabular}{c} **Max Length Problem** \\ **in Scenario** \\ \end{tabular} \\ \hline \multirow{4}{*}{Baldurs Gate II} & \multirow{2}{*}{80 \(\times\) 80} & AR0304 SR & 1734 & 79.42640686 \\ \cline{3-6}  & & AR0513 SR & 2073 & 78.15432892 \\ \cline{3-6}  & & AR0709 SR & 2048 & 75.01219330 \\ \hline \multirow{4}{*}{City maps} & \multirow{2}{*}{256 \(\times\) 256} & Boston & 47,768 & 379.5290039 \\ \cline{3-6}  & & Shanghai & 48,005 & 359.75945129 \\ \cline{3-6}  & & Berlin & 47,540 & 363.33304443 \\ \hline \multirow{4}{*}{Warcraft III} & \multirow{2}{*}{512 \(\times\) 512} & Harvest moon & 114,594 & 567.93311615 \\ \cline{3-6}  & & Scorched basin & 80,848 & 507.51175995 \\ \cline{1-1} \cline{2-6}  & & Dusk wood & 127,229 & 615.9625534 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Map related information table. mainstream algorithms is analyzed by comparing the path planning time, the number of grids in the traversed map, the length of the planned path, the computer resources consumed, and the turning angle of the path of each algorithm. Figure 6: Comparative experimental results of various algorithms on public dataset maps. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Map Name**} & \multirow{2}{*}{**Algorithm**} & \multicolumn{2}{c}{**Pathfinding**} & \multicolumn{2}{c}{**Number of**} & \multirow{2}{*}{**Path**} & \multirow{2}{*}{**Memory**} & \multirow{2}{*}{**Inputing**} \\  & & & **Time/s** & & **Tavversal** \\ \hline \multirow{4}{*}{Boston} & A* & 15.296216 & 16,573 & 365.8721 & 2,425,264 & 1035.00 \\ \cline{2-7}  & Dijkstra & 42.924916 & 47,688 & 393.2102 & 4,925,416 & 2250.00 \\ \cline{2-7}  & Theta* & 15.504178 & 16,573 & 354.5103 & 2,792,580 & 280.83 \\ \cline{2-7}  & W-Theta* & 0.892018 & 1576 & 358.4090 & 1,225,072 & 126.34 \\ \hline \multirow{4}{*}{Shanghai} & A* & 8.034565 & 11,632 & 344.5290 & 2,026,280 & 2205.00 \\ \cline{2-7}  & Dijkstra & 41.337722 & 47,792 & 354.4701 & 4,928,472 & 2160.00 \\ \cline{2-7}  & Theta* & 8.226009 & 11,632 & 332.0240 & 2,390,588 & 488.93 \\ \cline{2-7}  & W-Theta* & 0.535700 & 1260 & 333.6091 & 1,193,528 & 268.15 \\ \hline \multirow{4}{*}{Berlin} & A* & 18.947835 & 22,984 & 401.0732 & 2,948,536 & 5985.00 \\ \cline{2-7}  & [PERSON] & 42.740184 & 47,043 & 415.1564 & 4,882,776 & 2250.00 \\ \cline{2-7}  & Theta* & 19.215597 & 22,984 & 381.4792 & 3,320,892 & 389.47 \\ \cline{2-7}  & W-Theta* & 0.580014 & 1251 & 384.7610 & 1,205,720 & 266.51 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Experimental data sheet for various algorithms on City maps. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Map Name**} & \multirow{2}{*}{**Algorithm**} & \multicolumn{2}{c}{**Pathfinding**} & \multicolumn{2}{c}{**Number of**} & \multirow{2}{*}{**Path**} & \multirow{2}{*}{**Memory**} & \multirow{2}{*}{**Total Path**} \\  & & & **Time/s** & & **Tavversal** \\ \hline \multirow{4}{*}{Harvest moon} & A* & 0.053776 & 611 & 85.4975 & 249,720 & 405.00 \\ \cline{2-7}  & [PERSON] & 0.172302 & 1720 & 97.0955 & 252,208 & 450.00 \\ \cline{2-7}  & Theta* & 0.065306 & 611 & 81.3935 & 335,867 & 140.95 \\ \cline{2-7}  & W-Theta* & 0.03788 & 290 & 82.6155 & 222,792 & 140.95 \\ \hline \multirow{4}{*}{AR0513 SR} & A* & 0.199933 & 1473 & 86.1543 & 307,264 & 1170.00 \\ \cline{2-7}  & [PERSON] & 0.217634 & 2067 & 96.0955 & 356,432 & 540.00 \\ \cline{2-7}  & Theta* & 0.213901 & 1473 & 82.3920 & 387,939 & 183.73 \\ \cline{2-7}  & W-Theta* & 0.0660505 & 448 & 90.7401 & 223,744 & 121.00 \\ \hline \multirow{4}{*}{AR0709 SR} & A* & 0.077469 & 730 & 70.3553 & 248,408 & 1035.00 \\ \cline{2-7}  & [PERSON] & 0.223962 & 2026 & 82.7817 & 353,456 & 270.00 \\ \cline{2-7}  & Theta* & 0.087235 & 730 & 67.0026 & 329,115 & 198.43 \\ \cline{2-7}  & W-Theta* & 0.030227 & 253 & 68.0747 & 210,064 & 131.55 \\ \hline \hline \end{tabular}
\end{table}