# Research on Path Planning of Mobile Robot Based on Improved Theta* Algorithm
## 3 Simulation
### Experiment of Comparing W-Theta\({}^{\star}\) Algorithm with Other Algorithms  
This part of the experiment uses the Moving AI lab public dataset on three types of maps to compare various path algorithms, the maps are Baldurs Gate II map, urban map and Warcraft III map, and the details of each map are shown in Table 2.  
The Dijkstra algorithm, A* algorithm, Theta* algorithm, and W-Theta* algorithm were applied on each map for comparative experiments in terms of pathfinding time, number of traversed nodes, path length, and memory usage, and the visualization results of their path planning are shown in Figure 6. The solid purple line in the figure is the path planned by the Dijkstra algorithm, the solid red line is the path planned by the A* algorithm, the solid blue line is the path planned by the Theta* algorithm, the dashed yellow line is the path planned by the W-Theta* algorithm, the green dot in each map indicates the starting point, the red dot indicates the end point. The white area is the passable area, and the other color grids represent different obstacles. The relevant data of this part of the experiment are shown in Tables 3-5. The performance of the proposed W-Theta* algorithm and other \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Map Size/m\({}^{2}\)**} & **Obstacle** & **Algorithm** & **Pathfinding Time/s** & \
\begin{tabular}{c} **Number of** \\ **Tavessal** \\ **Nodes** \\ \end{tabular} & **Path** &
\begin{tabular}{c} **Memory** \\ **Consumption/Bit** \\ \end{tabular} \\ \hline \multirow{4}{*}{\(40\times 40\)} & \multirow{2}{*}{10\%} & W-Theta* & 0.017162 & 181 & 56.2899 & 39,483 \\ \cline{3-6}  & & Theta* & 0.030727 & 199 & 56.2899 & 40,971 \\ \cline{2-6}  & \multirow{2}{*}{30\%} & W-Theta* & 0.013585 & 190 & 58.7589 & 55,331 \\ \cline{3-6}  & & Theta* & 0.020874 & 314 & 57.7190 & 65,555 \\ \cline{3-6}  & \multirow{2}{*}{50\%} & W-Theta* & 0.025756 & 205 & 63.0570 & 71,531 \\ \cline{3-6}  & & Theta* & 0.068320 & 518 & 62.2417 & 96,451 \\ \hline \multirow{4}{*}{\(80\times 80\)} & \multirow{2}{*}{10\%} & W-Theta* & 0.013979 & 378 & 114.4069 & 121,179 \\ \cline{3-6}  & & Theta* & 0.229164 & 1045 & 115.6518 & 183,1279 \\ \cline{2-6}  & \multirow{2}{*}{30\%} & W-Theta* & 0.029807 & 343 & 118.3512 & 177,675 \\ \cline{3-6}  & & Theta* & 0.199758 & 1344 & 115.8627 & 258,171 \\ \cline{2-6}  & \multirow{2}{*}{50\%} & W-Theta* & 0.037211 & 356 & 130.4743 & 234,675 \\ \cline{3-6}  & & Theta* & 0.221151 & 1731 & 123.3626 & 344,867 \\ \hline \multirow{4}{*}{\(120\times 120\)} & \multirow{2}{*}{10\%} & W-Theta* & 0.054977 & 570 & 170.3327 & 246,419 \\ \cline{3-6}  & & Theta* & 0.707187 & 2385 & 170.1267 & 391,355 \\ \cline{1-1} \cline{2-6}  & \multirow{2}{*}{30\%} & W-Theta* & 0.053313 & 487 & 176.7601 & 371,787 \\ \cline{1-1} \cline{2-6}  & & Theta* & 0.980309 & 3688 & 175.7588 & 625,867 \\ \cline{1-1} \cline{2-6}  & \multirow{2}{*}{50\%} & W-Theta* & 0.060754 & 444 & 186.6482 & 492,251 \\ \cline{1-1} \cline{2-6}  & & Theta* & 0.666634 & 3104 & 180.2422 & 705,835 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Experimental data table of W-Theta* algorithm and Theta* algorithm for maps with three sizes and different obstacle densities.