# RRT*-Fuzzy Dynamic Window Approach (RRT*-FDWA) for Collision-Free Path Planning
## 1 Introduction  
In the field of automatic navigation of wheeled mobile robots, path planning is a frequently researched area. The main goal of a path planning algorithm is to plan a collision-free path from the initial state to the target in the constructed space of the robot [1]. Path planning is divided into global path planning and local path planning. Global planning [2; 3; 4] is able to accomplish the task in known static environments. However, environments and obstacles change dynamically in most navigation processes. When a mobile robot performs tasks according to global path planning, it must use various devices on board, such as lidar, depth cameras, and IMUs, to sense the surrounding environment and its own state and quickly plan local collision-free paths. For navigation, robots therefore usually use a combination of global path planning and local path planning [5; 6; 7]. The Rapid Exploration Randomized Tree [8] (RRT) has been shown to be a very effective global path planning algorithm; RRT can plan paths quickly and simply by generating a tree structure at high-speed increments in the construction space to find a goal. However, RRT algorithms also possess some constraints, such as not having asymptotic optimality [9; 10] and an inability to avoid dynamic obstacles; variants of improved RRT algorithms have, therefore, been proposed. [PERSON] [11] et al. proposed a \"Post-Triangular Rewiring\" method, which reduces the path planning time, improves efficiency, and creates an algorithm close to the global optimum. [PERSON] [12] et al. proposed a dual-tree fast exploration random tree (DT-RRT) algorithm to decrease the computational complexity of the RRT. In addition, DT-RRT reduces the length of the path and increases the coverage of the sampling points. [PERSON] et al. proposed an RRT* [13] algorithm which can make the path asymptotically optimal. [PERSON] et al. [14] introduced the dual-tree structure into an RRT* algorithm, thereby creating separate extension and optimization processes and improving the convergence speed. In addition, some scholars have attempted to improve global path planning methods such as RRT* to avoid dynamic obstacles. [PERSON] et al. [15] applied the RRT* algorithm to dynamic environments and introduced Paretotheory to propose a multi-objective dynamic fast exploration stochastic algorithm (MOD-RRT*), which improved the effective performance of the RRT* algorithm in avoiding unknown obstacles. However, there are many limitations in global path planning and dynamic environments. Compared with static environments, there are many uncertainties, such as randomly moving obstacles. It is, therefore, very difficult to predict the movement path of obstacles. Thus, local path planning in dynamic environments is currently an area of great research interest. In recent years, researchers have proposed many local path planning algorithms, such as the dynamic window approach [16] (DWA) and the artificial potential field method [17] (APF). Furthermore, [PERSON] [18] et al. proposed a collision avoidance algorithm based on the D*Lite algorithm for mobile robots; this algorithm was applied to a logistics delivery scenario to effectively avoid collision and safely reset the robot's optimal movement route when the robot encounters a crossover situation at an intersection. [PERSON] [19] et al. proposed a combination of the sine cosine algorithm and ant colony algorithm for multiple environments such as static and dynamic, and applied the algorithm in multi-robot formations. [PERSON] [20] et al. constructed a risk region of dynamic obstacles using the Kalman filter state estimation, combining it with a nonlinear model predictive control to achieve safe obstacle avoidance. DWA has been extensively applied because of its dynamic characteristics combined with those of the robot. Later, [PERSON] [21] et al. proposed an adaptive rolling window method based on the edges of obstacles and the target point, which has good safety and environmental applicability. [PERSON] [22] et al.