# Obstacle Avoidance in a Three-Dimensional Dynamic Environment Based on Fuzzy Dynamic Windows
## 1 Introduction
proposed a conditional deep Q-network with fuzzy logic, which aims to handle the issues of directional planning in end-to-end autonomous driving systems and the independence of different motion commands. This approach has better learning performance and driving stability performance, but it does not take into account obstacles such as cars and pedestrians [24]. Whether it is a graph-based search method or a local navigation algorithm, they mostly aim at a flat environment. For path planning in a space environment, popular approaches are mainly to integrate obstacles, speeds, and path lengths into constraints and generate trajectories by curve parameterization [25; 26]. Most of the numerical methods use path point parameterization to define splines, polynomials, and so on. However, for nonlinear problems, these parameterization algorithms require a lot of computing resources. Without further assumptions or simplifications, these methods are not suitable for solving the problem of dynamic obstacles. Then, based on a local parameterized guidance vector field, [PERSON], [PERSON] et al. proposed a method that can generate a constant velocity vector field by the decomposition of unmanned aerial vehicle (UAV) kinematics into normal and tangential components with respect to the obstacle boundary [27]. This method can effectively avoid static obstacles and dynamic obstacles. However, it also has one limitation; that is, it assumes that agents are at a constant height and hence simplifies the three-dimensional (3D) problem to a two-dimensional (2D) problem. Due to the different power modes provided by the thrusters, the problems of the UAV and the space agent in obstacle avoidance and trajectory planning are not completely the same. However, in terms of multi-objective path planning [28; 29], collaborative path planning [30; 31] and cluster motion [32], they have similar path planning problems. Based on the Legendre polynomial method, [PERSON], [PERSON] et al. proposed the ASTRO (Admissible subspace trajectory optimizer) method which transforms the complex cost function into a simple convex form and applied it to cope with the problem of optimizing real-time three-dimensional (3D) trajectory [33]. Nonetheless, when the constraints are complex, the numerical method still has the problem of local minima in the optimization process. To address the navigation problem in the three-dimensional environment, this paper proposes a fuzzy dynamic window approach (DF_DWA). According to the traditional DWA, it is believed that the values of 0.8, 0.1, and 0.1 for the parameters of azimuth, obstacle clearance, and speed, respectively can provide good results in some situations [2]. Nevertheless, as the environment becomes more complex, this set of weights is not suitable in all situations. Different working environments using the same weight coefficient will result in obstacle avoidance failure or make the machine stop working [15]. [PERSON], [PERSON] et al. suggested using fuzzy logic to update the weight of DWA objective function by analyzing the distribution of eight obstacles [34]. [PERSON], [PERSON] et al. simplified the distribution of obstacles to three situations, thereby reducing the number of fuzzy logic rules, and improving computational efficiency [35]. However, the two methods mentioned update the weight of the objective function only by the distribution of obstacles, without considering the distance of the obstacles. As a result, the robot can easily fall into U-shaped obstacles or the local minima [36; 37]. Moreover, the existing objective function does not consider the pointing problem when the agent approaches the target. In this article, by adding the term of the distance target, a new objective function is established to eliminate the influence of angle orientation. The weight parameters are adjusted by fuzzy logic so that the space robot can adapt to environmental changes. The dual dynamic window method and local goal method are used to avoid the agent trapping in the local minima and U-shaped obstacles.