## 4 Experimental Results
There may be a significant difference between the performance observed visually and the numerical results in the table for one of the repeated trials. The form of the planned path for each algorithm is shown in the figure for visual reference. Furthermore, the proposed post triangular processing of the midpoint interpolation method is used to see whether there is a region where the piecewise linear path is smoothed. The path planning results are shown in Figure 9 for Map 1 among the specified environment maps for each algorithm. In terms of appearance, the one to which the post triangular processing of the midpoint interpolation method (\(\varepsilon\): 10 px) was applied seems to have a smoother slope compared to those of the other algorithms, and the path length with the method (\(\varepsilon\): 10 px) seems to be the shortest. \begin{table}
\begin{tabular}{c c} \hline \hline
**H/W** & **Specification** \\ \hline CPU & Intel Core i7-6700k 4.00 GHz (8 CPUs) \\ RAM & 32,768 MB (32 GB DDR4) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Computer performance for simulation. The path planning results (average values after repeating the trial 100 times) are shown in Table 2 for Map 1 among the specified environment maps for each algorithm. When applying the post triangular processing of the midpoint interpolation method (\(\varepsilon\): 10 px), the path length becomes 62% (1224/1994(%)) compared to the RRT, which is the shortest of all the algorithms, and the planning times are all similar. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Performance** & **RRT** & \begin{tabular}{c} **Proposed Method** \\ **(\(\varepsilon\): 50 px)** \\ \end{tabular} & \
\begin{tabular}{c} **Proposed Method** \\ **(\(\varepsilon\): 30 px)** \\ \end{tabular} &
\begin{tabular}{c} **Proposed Method** \\ **(\(\varepsilon\): 10 px)** \\ \end{tabular} \\ \hline Path length (px) & 1944 (100\%) & 1403 (72\%) & 1325 (68\%) & 1224 (62\%) \\ Planning time (ms) & 697 (100\%) & 698 (100\%) & 698 (100\%) & 698 (100\%) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Experimental results of Map 1 (numbers in parentheses (averages of repeating trial 100 times) are relative ratios to RRT results (values less than 1 are counted as 1)). Figure 9: Experimental results of Map 1: (**a**) RRT; (**b**) proposed method (\(\varepsilon\): 50 px) applied; (**c**) proposed method (\(\varepsilon\): 30 px) applied; (**d**) proposed method (\(\varepsilon\): 10 px) applied. The path planning results are shown in Figure 10 for Map 2 among the specified environment maps for each algorithm. In terms of appearance, the one to which the post triangular processing of midpoint interpolation method (\(\varepsilon\): 10 px) was applied seems to have a smoother slope compared to those of the other algorithms, and the path length with the method (\(\varepsilon\): 10 px) seems to be the shortest. The path planning results (average values after repeating the trial 100 times) are shown in Table 3 for Map 2 among the specified environment maps for each algorithm. By applying the post triangular processing of midpoint interpolation method (\(\varepsilon\): 10 px), the path length becomes 74% (730/986(%)) compared to the RRT, which is the shortest of all the algorithms, and the planning time is similar to that of the RRT algorithm when the method (\(\varepsilon\): 50 px) is applied. However, the absolute time difference is 1 ms, which seems to be large when the method is applied because it is an environment that requires less planning time. Figure 10: Experimental results of Map 2: (**a**) RRT; (**b**) Proposed method (\(\varepsilon\): 50 px) applied; (**c**) Proposed method (\(\varepsilon\): 30 px) applied; (**d**) Proposed method (\(\varepsilon\): 10 px) applied. The path planning results are shown in Figure 11 for Map 3 among the specified environment maps for each algorithm.