## 1 Introduction  
Currently, autonomous aerial vehicles perform various tasks, such as logistic [1, 2, 3], environment monitoring or target tracking tasks [4, 5, 6, 7]. In this paper, we consider the path planning of a fixed-wing autonomous aerial vehicle. Note that a fixed-wing aerial vehicle can freely move in 3D environments, not in 2D environments. Collision-free 3D path planning is important for the safe navigation of a fixed-wing aerial vehicle in obstacle-rich uncertain 3D environments [6, 8, 9, 10]. There can be physical obstacles, such as other aerial vehicles or buildings, as well as legal obstacles, such as areas where the drone is not allowed to fly (for example, airports, military areas, or government areas). This research therefore addresses a 3D path planner, which is time-efficient in generating a safe and short path to the destination. In practice, a fixed-wing aerial vehicle has a limited turn rate, due to its acceleration limits [11, 12, 13, 14, 15, 16, 17]. Regarding 2D environments, many papers [11, 12, 13, 15, 16, 17] considered a robot's path plan while considering the robot's acceleration limits. Regarding 2D environments, ref. [18] addressed an environment-guided variant of rapidly exploring random tree (RRT) designed for kinodynamic robot systems that incorporate a cost model to estimate the probability of collision under uncertainty in control and sensing. Regarding 2D environments, ref. [19] addressed a path-planning method for fixed-wing aerial vehicles based on the Theta-star algorithm. Ref. [19] used Euler spiral (or clothoids) to serve as connection arcs between nodes, mitigating trajectory discontinuities. Regarding 2D environments, ref. [13] addressed a fixed-wing aerial vehicle path planning algorithm for obstacle avoidance in cluttered environments. In [13], a path planning scheme was developed based on a Dubins-based improved vector field histogram for collision avoidance, satisfying the kinematic constraints of the fixed-wing aerial vehicle. Note that a fixed-wing aerial vehicle can freely move in 3D environments, not in 2D environments. In this paper, a 3D path plan algorithm is developed by considering a limited turn rate of a fixed-wing aerial vehicle. The authors of [20] described the boundary and pointing constraints of the spacecraft trajectory planning problem based on time and path optimization. Grey wolf algorithm was used for the path planning of a spacecraft in [20]. However, the computational load of a population-based meta-heuristics algorithm, such as the grey wolf algorithm, is too heavy for real-time applications. Moreover, dynamic models of a spacecraft are different from those of a fixed-wing airplane. The authors of [21] addressed a 3D path planner, considering maneuverability constraints of an aerial vehicle. Through computer simulations, we compared the performance of the proposed path planner with [21], in order to show the outperformance of the proposed 3D path planner. There are many research studies on 3D path plan algorithms for a robot [4]. Potential field [22], A-star algorithm [23; 24; 25; 26], and Theta-star algorithm [27; 28] can be used as 3D path plans for robots. Potential field can lead to a local minimum (not the global minimum) of the field, and thus, the robot may not reach its destination. A-star, Theta-star, or Djkstra algorithms [24; 25; 26; 27; 28] require that the entire domain consists of multiple grid cells. As one increases the domain volume, the number of grid cells required to cover the entire domain also increases. Therefore, calculating a path utilizing A-star, Theta-star, or Djkstra algorithms in a large 3D environment may not be feasible due to large computational load. In this paper, we consider a 3D workspace domain without grid cells. Considering a domain without grid cells, the RRT algorithms in [29; 30; 31] applied random sampling to find a path to the destination. The authors of [30] showed that the path constructed by RRT-star converges to the optimum path asymptotically as time reaches infinity.