## 1 Introduction  
The path-planning process of a mobile robot aims at finding a collision-free path to move the robot from the current posture to the goal posture [1; 2; 3]. If there are multiple available paths, the optimal path in the sense of an objective function, such as the minimum distance, can be chosen. The algorithms for mobile-robot path planning can be grouped into four categories: roadmap approaches, such as the visibility graph or generalized Voronoi graph; cell decomposition approaches, such as the vertical cell decomposition (VCD) or approximate cell decomposition; sampling-based planning methods, such as the rapidly exploring random tree (RRT) or probabilistic roadmap (PRM), and potential field methods [2; 3; 4; 5]. Among these methods, roadmap approaches are generally fast and easy to implement, but an intrinsic way to describe environmental information is not provided [1; 2; 3]. Sampling-based planning methods are more practical, but they do not provide completeness so we cannot recognize the non-existence of a path [2; 3]. Potential field methods are useful to control the robot by generating a differentiable smooth path, but they cannot give explicit information on the roadmap and easily fall into a local minimum [1; 2; 3]. There are also some hybrid approaches, such as a potential field with RRT [6] or potential field with cell decomposition [7].  
Cell decomposition, which is a classical and representative method for mobile-robot path planning, decomposes the given environment into several cells and finds a collision-free path based on the connectivity graph of these cells [2; 3; 4; 5; 6; 7; 8; 9; 10]. Here, each node of a connectivity graph is made by the representative point of each cell or its border line. Each link of the connectivity graph between the nodes indicates that the corresponding cell is adjacent to each other [11]. In various cell decomposition algorithms [12; 13; 14; 15; 16; 17], one of the most widely known algorithms is vertical cell decomposition (VCD), but it does not generate an efficient path because it uses too many cells [8]. Figure 1 shows an example of the previous exact cell decomposition using VCD. VCD makes vertical lines from the convex vertices to decompose the environment into cells. The adjacency relationship among the cells is represented by the connectivity graph and used to find a path using graph search algorithms. VCD does not guarantee the optimality of the number of decomposed cells since there is no consideration of the shape of the obstacle. Reducing the number of decomposed cells directly increases the efficiency in path planning, but finding the optimal decomposition case is known as an NP-hard problem [1; 2; 3].  
To supplement this drawback, the Opposite Angle-based Exact Cell Decomposition (OAECD) [18] was proposed by using a type of greedy approach to minimize the number of cells and increase efficiency. However, the OAECD can only be applied for polygonal obstacles, since it is operated based on the relationship among the vertices of the obstacles. In other words, path planning in an environment with curvilinear obstacles is impossible by itself. Therefore, in this paper, a novel expanded polygonal approximation method based on Douglas-Peucker (DP) algorithm is proposed to apply OAECD path planning to the cases with curvilinear obstacles.  
In Chapter 2, a novel polygonal approximation algorithm for curvilinear obstacles is addressed. Then, the algorithm is applied to a modified OAECD algorithm in Chapter 3. The experimental results are shown in Chapter 4, and the paper is concluded in Chapter 5.