## 4 Experimental Results  
The path between the RRT in various environment maps through simulation and the RRT algorithm to which the proposed post triangular processing of the midpoint interpolation method is applied were used to validate the performance of the method proposed in this paper, and the path planning results were compared. The performance measures compared were the average values after repeating the trial 100 times (sampling position was changed for each trial) of the path length (px) and the planning time (ms) of the first complete path (the first complete path to reach a destination point from a starting point). Various environment maps have been examined and used to validate the performance of the proposed path planning algorithms in related works. Since the efficiency of the performance measures expected during the experiment varies somewhat based on the composition of obstacles (e.g., number, location, shape), it is important to choose which environment map to utilize carefully. Figure 7: Flowchart of post triangular processing of midpoint interpolation method. The four environment maps used in the experiment are shown in Figure 8. The four environment maps were created by partially referring to the experimental environment proposed by [PERSON] in 2017 [21]. All environment maps were 600 \(\times\) 600 px in size, with a 30 px step length. The start points (S) are represented by green circles, while the destination points (G) are represented by purple circles. Obstacles are black polygons with yellow contours (blue in the experimental results). Map 1 of Figure 8a appears to be an efficient environment for validating optimality and completeness but a weak environment for sampling-based path planning algorithms like the RRT algorithm. Many samplings are required since the probability of finding a solution is low. Map 2 of Figure 8b appears to be an efficient environment for validating the optimality and completeness of the path planning algorithm. Map 3 of Figure 8c is an environment that is efficient for validating the optimality and the planning time of the  
Figure 8: Environment maps for experiments: (**a**) Map 1; (**b**) Map 2; (**c**) Map 3; (**d**) Map 4.  
path planning algorithm, as it consists of obstacles (50 vertices) that approximate circles. Map 4 of Figure 8d is an environment that is efficient for validating the optimality and the planning time of the path planning algorithm but a weak environment for sampling-based path planning algorithms such as the RRT algorithm. The number of samples and planning time required increase drastically when the path to the destination point is narrow or there are few entrances since the sampling-based path planning algorithm depends on probabilistic completeness. The specification of the computer used in the simulation is shown in Table 1. The simulator used for the simulation [8] was developed based on C# WPF (Microsoft Visual Studio Community 2019 Version 16.1.6 Microsoft.NET Framework Version 4.8.03752), and only a single thread was used for calculations except for the visual part. Generally, depending on the specification of the computer, the result of performance measurements, such as planning time, may vary during the simulation. We validate the experimental results (path length, planning time) in the four environment maps in which the post triangular processing of the midpoint interpolation method (\(\varepsilon\): 50, 30, 10 px) is applied to the RRT algorithm and its path planning results. Since \(\varepsilon\) requires a higher amount of computation as it gets smaller, it was set to a value close to the 30 px step length of the experimental environment. The experimental results for each map consist of a figure and table. The figure is a path planning result for each algorithm shown in the case of a single trial (the figure for each algorithm is not the result of repeated trials). The table shows an average value of the results of planning time and path length from the path planning repeated trials.