## 1 Introduction  
Unmanned aerial vehicles (UAVs) have recently been used in several fields to perform various missions, such as search and rescue [1], surveillance [2], monitoring [3], delivery [4], and inspection [5]. UAVs are being increasingly used due to their cost efficiency, high reliability, and good performance. These needs lead to an increased demand for UAV airspace and an increased risk of collisions in that limited airspace. To perform successful missions and reduce the risk of collisions, the safe operation of UAVs must be ensured. That is, UAVs must equip a certain sensing system to detect threats and have a collision avoidance (CA) system to avoid threats without collision. This is called sense and avoid for UAVs [6]. Among several CA techniques, one of the most widely used algorithms is the artificial potential field (APF) method [7]. With its simple principle, the APF efficiently provides a smooth and safe trajectory. However, the APF faces some problems when one or multiple obstacles block an agent's path toward the goal position with the symmetric pattern or obstacles are located near the goal position. The former is called local minima, and this generally occurs when obstacles are exactly located between the agent and the goal location. The latter is called the goal non-reachable obstacles nearby (GNRON) problem. Indeed, when the goal location is within the influence of the repulsive potential field, the agent faces a GNRON situation. Several researchers have attempted to resolve these two issues by applying other techniques or modifying formulations. Some researchers have combined the APF with other existing algorithms. As an illustration, [PERSON] et al. [8] used the rapidly-exploring random tree method as a global planner in the presence of static obstacles to generate a global path that does not encounter the local minima and GNRON problems and then applied the APF as a local planner to the global path generated beforehand. In Ref. [9], a bug algorithm was introduced to resolve the issues when the agent faces local minima or GNRON situation. Moreover, to deal with these issues, other scholars have suggested making modifications of the potential functions or fields of the APF. [PERSON] et al. [10] modified the repulsive potential field formulation by adding a fractional term and another term with the signum function to solve the local minima and GNRON problems, respectively. In Ref. [11], the relative distance between an agent and a goal location was multiplied to the repulsive potential function to resolve the GNRON problem. Furthermore, the local minima problem was resolved by multiplying a term with exponential functions into the repulsive potential function. In Ref. [12], a fuzzy inference system based on the APF was considered to deal with the local minima problem. Furthermore, [PERSON] et al. [13] revised the repulsive potential field formulation by multiplying an additional term and combining it with the rolling window approach to resolve the APF's two issues, and the intermediate target position was used to avoid obstacles. In addition, exponential functions [14] and Gaussian-like functions [15] have been utilized to formulate attractive and repulsive potential fields. [PERSON] et al. [16] introduced the concept of the curl-free vector field to resolve the local minima issue. Although several researchers have proposed various techniques for resolving the APF's issues, the aforementioned approaches have been applied in a two-dimensional (2D) environment and are not suitable in a situation where the 3D motion of UAVs has to be considered. This research proposes a CA approach based on an enhanced potential field (EPF) building on the authors' previous work developed in 2D environments to expand to become applicable to 3D environments by combining the horizontal and vertical avoidance maneuvers.