# TA-RRT*: Adaptive Sampling-Based Path Planning Using Terrain Analysis
## 4 Experiment
### Experiment in Static Scenarios  
#### 4.2.1 Performance Comparison  
In this section, we evaluate the performance of each algorithm by analyzing the path planning results across simple, intermediate, and complex environments. Figure 6 shows the path planning results of the RRT*, Informed-RRT*, RRT*-Smart, and TA-RRT* algorithms in a simple environment. Blue and green dots represent the start and goal points, respectively. Gray areas indicate obstacles, black lines show the expanded trees, and purple lines indicate the final paths. RRT* tends to generate nodes uniformly across the entire map due to its sampling method. Informed-RRT* tends to concentrate new nodes within the ellipse, while the RRT*-Smart focuses nodes around key points, such as the vertices of obstacles. The proposed TA-RRT* tends to concentrate nodes along the straight lines connecting obstacle vertices, guided by \(\epsilon\)-greedy-based sampling, although some nodes are still generated across the map. Figure 7 and Table 1 present the results from 100 repeated experiments in a simple environment. M1 to M4 represent RRT*, Informed-RRT*, RRT*-Smart, and TA-RRT*, respectively. Informed-RRT* demonstrates the shortest average path length, even with a relatively small number of nodes, due to effective sampling within the elliptical region. However, its average execution time is the longest due to node concentration in a narrow area. On the other hand, RRT*-Smart shows a relatively long average path length and high  
Figure 6: Examples of path planning results in a simple 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. standard deviation, as there are insufficient corners to serve as beacons, making it difficult to effectively sample additional nodes. TA-RRT* demonstrates path planning performance comparable to Informed-RRT*, even in simple environments. In addition, TA-RRT* shows the highest average number of nodes, indicating that it was able to use more nodes to improve the path. Figure 8 shows the path planning results in the intermediate environment. It is hard to observe a similar tendency for node concentration in a confined area with Informed-RRT* in the intermediate environment, as the elliptical sampling region expands when the path does not follow a straight line. RRT*-Smart aims to produce straighter paths through its optimization process. However, as shown in Figure 8c, the algorithm may struggle to make significant corrections when the environment imposes complex path adjustments, potentially leading to less efficient paths. In contrast, TA-RRT* effectively improves the path through terrain analysis-based sampling, allowing for more consistent and efficient improvements in the path, even in challenging terrains. Figure 9 and Table 2 present the results from 100 repeated experiments in an intermediate environment. Due to the winding path, Informed-RRT* finds it difficult to effectively improve the path through additional sampling within the elliptical region, resulting in a relatively long average path length. TA-RRT* uses terrain analysis-based sampling to effectively improve the path, resulting in the shortest average path length and a small standard deviation, indicating high stability in path planning. Figure 10 shows the path planning results in a complex environment. As shown in Figure 10d, TA-RRT* utilizes terrain analysis-based sampling to effectively distribute nodes, including areas near the goal point. This approach enables TA-RRT* to maintain robust exploration and identify the shortest paths more efficiently, even in the presence of complex obstacles. In contrast, other algorithms tend to have insufficient sampling near the target point, which can make it challenging to find the optimal path.