# TA-RRT*: Adaptive Sampling-Based Path Planning Using Terrain Analysis
## 4 Experiment
### Experiment in Static Scenarios
#### 4.2.1 Performance Comparison
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Exec. Time (ms)**} & \multicolumn{2}{c}{**Path Length**} & \multicolumn{2}{c}{**No. of Nodes**} \\ \cline{2-7}  & **Average** & **STD** & **Average** & **STD** & **Average** & **STD** \\ \hline M1 & **7428.15** & 255.28 & 11.72 & 0.03 & 2809.54 & 16.58 \\ \hline M2 & 12,768.33 & 757.05 & **11.68** & 0.01 & 2325.18 & 30.84 \\ \hline M3 & 11,315.65 & 4383.81 & 12.08 & 0.35 & 1887.46 & 195.07 \\ \hline M4 & 9699.26 & 973.86 & 11.71 & 0.01 & **2864.34** & 17.49 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Path planning results in a simple environment. Figure 7: Box plots expressing the path length distributions of the path planning algorithms in a simple environment. Figure 8: Examples of path planning results in an intermediate environment. (**a**) RRT\({}^{*}\). (**b**) Informed-RRT\({}^{*}\). (**c**) RRT\({}^{*}\)-Smart. (**d**) TA-RRT\({}^{*}\). The blue and green dots represent the start and goal points, and the purple line represents the resulting path. Figure 9: Box plots expressing the path length distributions of the path planning algorithms in an intermediate environment. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Exec. Time (ms)**} & \multicolumn{2}{c}{**Path Length**} & \multicolumn{2}{c}{**No. of Nodes**} \\ \cline{2-7}  & **Average** & **STD** & **Average** & **STD** & **Average** & **STD** \\ \hline M1 & 4739.59 & 847.60 & 29.80 & 0.63 & 1450.52 & 120.25 \\ \hline M2 & 4347.52 & 705.95 & 30.11 & 0.72 & 1354.07 & 112.00 \\ \hline M3 & **3326.30** & 362.02 & 30.01 & 0.77 & 1301.64 & 90.78 \\ \hline M4 & 8301.36 & 1034.96 & **29.27** & 0.27 & **2167.50** & 133.16 \\ \hline \hline \end{tabular}  
* Values highlighted in bold represent the best performance.  
\end{table} 
Table 2: Path planning results in an intermediate environment. Figure 11 and Table 3 show the performance results obtained from 100 repeated experiments in a complex environment. RRT* generally produced short paths, but the high standard deviation in path length indicates low path stability. Due to the simplicity of the path exploration, the average execution time was the shortest. Informed-RRT* had a short average path length, but the large standard deviation resulted in low path consistency. Although the average execution time was short, it struggled with path optimization in complex environments. RRT*-Smart attempted to optimize the path through additional sampling and path update, but it resulted in a long average path length with a high standard deviation. Despite the increased execution time, it showed limitations in effective path exploration. In contrast, TA-RRT* demonstrated the shortest average path length through terrain analysis-based sampling. The low standard deviation in path length indicates high path consistency, showing that TA-RRT* performs excellently even in complex environments. As a result, Informed-RRT* and RRT*-Smart improve path optimality by sampling regions likely to lie on the shortest path, such as the elliptical area around the line connecting two points or areas near terrain vertices, based on empirical observations. These algorithms can generate more optimal paths than conventional RRT*, from simple to complex environments, depending on their underlying assumptions. The TA-RRT* proposed in this paper demonstrates through experiments that it can derive more optimal paths across various environments by sampling more nodes in valid regions based on terrain analysis. Figure 10: Examples of path planning results in complex environments. (**a**) RRT*. (**b**) Informed-RRT*. (**c**) RRT*-Smart. (**d**) TA-RRT*. The blue and green dots represent the start and goal points, and the purple line represents the resulting path.