# Obstacle Avoidance in a Three-Dimensional Dynamic Environment Based on Fuzzy Dynamic Windows
## 1 Introduction  
It is expected that space autonomous robotics will be used to complete complex and dangerous tasks in space as space technology develops [1]. As a robot completes a mission, it needs to plan a safe trajectory from a starting point to a target point. Collisions and path optimization are the main issues relating to the planning of the trajectory (i.e., navigation). Currently, navigation algorithms fall into two categories: global planning algorithms and local navigation algorithms. Previous studies have also combined the above two types of algorithms to achieve better navigation, but such a combination depends on the robot's autonomy and environmental factors [2]. Some notable global navigation algorithms avoid the collision problem by building a global environment map: e.g., A* [3], D* [4], FD* [5], and RRT [6]. When planning a path on a map, the optimization goal is usually the shortest path or the lowest energy use. However, considering that in the planning process, the speed, and accuracy of graph-based search methods depend on the granularity of the search space, those approaches are not suitable for real-time application. To improve real-time performance, some studies have proposed local navigation algorithms. Currently, the simplest local navigation algorithms are bug-based algorithms, e.g., bugI, bug2 [7], and tangent bug [8]. When the robot encounters an obstacle, the robotwill move along the boundary of the obstacle until it avoids the obstacle. The classical reactive navigation methods include the VFH (vector field histogram) [9] and its extended versions VFH+ [10] and VFH* [11], which are all based on the virtual vector field method. The moving direction of histogram methods is given by dividing the surrounding environment into different angular sectors of the polar histogram and the next direction of the robot's movement is obtained according to the proximity of an obstacle. Another classical reactive navigation method is the velocity space approach. This approach uses the evaluation function such as safety and smoothness to calculate the next movement direction. Some well-known velocity space algorithms are dynamic-window approach (DWA) [12; 13] and curvature velocity method (CVM) [14]. As for the nonlinear problem of moving obstacles, [PERSON] and [PERSON] [2] proposed an extension of the DWA algorithm (i.e., the time-varying dynamic-window algorithm), where the moving obstacles are modeled as moving cells in a gridded map. Considering the time factor in the process of obstacle avoidance, [PERSON] et al. proposed DW4 DO and DW4 DOT methods based on CVM (curvature velocity method) to plan a safer and longer obstacle avoidance path [15], and applied the methods in a dynamic environment. However, the main drawback of the local navigation algorithms is the local minima, especially in the use of U-shaped obstacles. One approach of avoiding the local minima problem is to select a local target of the robot's surroundings and calculate the direction of the next step. Lane-Curvature Method (LCM) [16] and Beam-Curvature Methods (BCM) [17] algorithms are representatives of this approach and are based on the CVM algorithm. The LCM algorithm obtains the local target by dividing the channel, whereas the BCM obtains the local target by dividing the sector. [PERSON], [PERSON] et al. proposed a hybrid dynamic window approach that can avoid the agent falling into the local minima, which is superior to DWA [18]. [PERSON], [PERSON] et al. proposed a dynamic window method with virtual goal in dynamic environments, which can make the robot escape the concave trap [19]. In addition to these algorithms, there are evolutionary algorithms that are based on neural networks or fuzzy logic [20; 21; 22]. [PERSON], [PERSON] proposed a hybrid intelligent approach that combines fuzzy logic and genetic algorithm to enable robots to quickly find an optimal path that avoids rough areas, which effectively solves the path planning of highly mobile robots in rough environments [23]. [PERSON], [PERSON] et al.