## 1 Introduction  
Recent path planning research for the robot has encompassed a wide range of topics [1, 2]. Path planning is an important capability for autonomous mobile robots. A robot must be able to identify a path from its current position to its destination in order to move successfully. A mobile robot must be able to discover an optimal or sub-optimal collision-free path in the environment from the starting position to the destination [3]. Path planning is the formulation of a route for a mobile robot to proceed from a starting point to a destination point in Euclidean space as efficiently as possible while avoiding both static and dynamic obstacles and maintaining optimality, clearance, and completeness [4]. An optimal path is one with the ideal path length, a clear path is one without obstacles for the mobile robot to collide with, and a complete path is one in which the robot can move from the start point to the destination point without colliding with obstacles. Furthermore, it is indeed possible for the robot to be able to optimize its path by determining the quickest and safest path to its destination point in order to save time and energy. However, an algorithm that generates the optimal path increases the computation, and an algorithm that quickly generates a path does not guarantee the optimal path [5]. It is difficult to ensure optimality with the sampling-based rapidly-exploring random tree (RRT) algorithm [6]. As shown in Figure 0(a), the RRT algorithm is a path planning algorithm that involves repeatedly adding a randomly sampled position as a child node in a tree with the starting point as the root node until the destination point is reached. The tree extends out in the shape of a stochastic fractal, as shown in Figure 0(b), and has an algorithm used to locate the destination point. The RRT algorithm and other sampling-based algorithms [7, 8] offer the benefit of planning a path in a shorter time with less computing than traditional path planning algorithms like the visibility graph- [9], cell decomposition- [10], and potential field-based algorithms [11]. On the other hand, it does not ensure optimality and has the drawback of having probabilistically assured completeness. The latter is also known as probabilistic completeness [12], which implies that completeness is assured when the number of random samples is infinite but not always when the number of random samples is limited. The goal of this research is to enhance the RRT algorithm, which ensures completeness and performs better than the related algorithms. To solve these problems, the main idea of the proposed post triangular processing of midpoint interpolation method is effective in path planning algorithms that do not guarantee optimality, such as the RRT algorithm that has a locally piecewise linear shape and can be used as a post-processing method after a path has been planned using one of these algorithms. It may also be used for different route planning methods since it is a post-processing technique that has no impact on calculation time. The sampling-based path planning algorithm's primary strength is the fast planning speed based on the small amount of computation compared to the traditional path planning algorithms [7]. Performance verification using simulation in various environments and mathematical modeling were used to validate the performance of the proposed method in this paper. The case in which the proposed algorithm is applied to the sampling-based path planning method and the case in which it is not applied are compared through simulation. Here, the planning time and path length of the first complete path to reach a destination point from a starting point are evaluated. This paper is organized as follows: Section 2 reviews some related works. Section 3 introduces the proposed post triangular processing of the midpoint interpolation method. Various experimental environments are constructed for path planning in Section 4 to examine the effectiveness and improvements of the proposed method.