# TA-RRT*: Adaptive Sampling-Based Path Planning Using Terrain Analysis
## 1 Introduction  
The development of unmanned vehicle technologies, from drones to autonomous vehicles and robots, has rapidly expanded into both civilian and military applications [1, 2, 3, 4, 5, 6]. To enhance the autonomy of these vehicles in various environments, extensive research has focused on situational awareness and planning. However, significant technical challenges remain, such as navigating complex terrains, predicting dynamic obstacles, and adapting to environmental changes in real-world scenarios [7, 8]. Addressing these challenges requires transforming 2D perception data from sensors like cameras, LiDAR, and radar into practical 2D Bird's Eye View (BEV) images. This transformation is crucial for enabling path planning and control algorithms that help unmanned vehicles navigate complex environments [9]. This study focuses on path planning for unmanned vehicles, aiming to generate routes that avoid obstacles and efficiently reach their destinations based on maps created through BEV images. Path planning algorithms have been extensively researched and can be broadly categorized into graph search and sampling approaches [10, 11, 12]. Graph search-based path planning relies on a pre-constructed graph using previously acquired environmentalinformation, enabling relatively fast shortest-path searches. However, in many unmanned vehicle operations, obtaining and constructing such information in advance is often challenging. Consequently, significant research has focused on methods that explore paths to the target point through random sampling. Rapidly exploring Random Tree (RRT) [13] and Probabilistic RoadMap (PRM) [14] are representative sampling-based path planning algorithms. RRT explores paths by expanding a tree structure through random sampling, and can find a path to the target point with a high probability when a sufficient number of nodes are sampled. However, it does not guarantee optimality. The path optimality is primarily defined in terms of cost, which generally includes factors such as path length, energy consumption, and so on. RRT* improves upon RRT by restructuring the tree during node expansion, thereby enhancing the optimality of the explored path [15]. Since the introduction of RRT*, various modified algorithms have been developed to further enhance path optimality [16; 17; 18; 19]. Although RRT* can find a path that connects the starting point to the goal, the generated path is not always the shortest. To address these limitations, algorithms such as Informed-RRT* and RRT*-Smart have been proposed [17; 18]. Informed-RRT* generates an initial path, then defines an ellipse using the start and goal points, along with the path length, as parameters [17]. Additional nodes are sampled within this ellipse to improve the initial path, with the ellipse being iteratively reconfigured to further enhance path efficiency. RRT*-Smart also generates an initial path and improves it by designating key points in the environment, such as terrain corners, as beacons [18]. Additional nodes are sampled near these beacons to update and improve the path. Although these algorithms propose additional sampling regions based on environmental analysis, their ability to improve paths is evident under certain conditions, but may be limited in complex terrains. Therefore, in this paper, we propose a terrain analysis (TA)-RRT* algorithm which enables effective path planning through terrain analysis. The key features of the proposed algorithm are as follows: First, a probability density function (PDF) is generated based on terrain analysis, and adaptive sampling is applied using this PDF to expand the tree. This approach allows for more effective path reconfiguration. Next, the step size is adaptively adjusted according to the complexity of the terrain. In more complex terrains, a shorter step size is used, which enables more linear connections between nodes and improves the optimality of the generated path. This paper is structured as follows: Section 2 analyzes existing RRT*-based path planning algorithms.