This paper presents a new fuzzy potential system to plan the motion of Unmanned Aerial Vehicles (UAVs) in dynamic 3D Space. The system consists of two fuzzy subsystems representing the attractive model and the repulsive model of virtual forces in 3D. The attractive model will generate the attractive force required to pull the UAV in a smooth and optimized trajectory to land softly on a moving or stationary target. The repulsive model will generate the required repulsive force to avoid stationary or moving obstacles in 3D Space. The attractive fuzzy inference system takes the relative position and relative velocity between UAV and the target in the x, y, and z directions as inputs. It generates the required attractive force in the x, y, and z directions. The repulsive fuzzy inference system takes the relative position between UAV and obstacle in the xyz directions as input. Fuzzy associative memory (FAM) models the inputs and generates the required repulsive force in the x, y, and z directions. As a result, the UAV is considered to be moving under the influence of fuzzy virtual attractive and repulsive forces simultaneously. Accordingly, it will be able to change both its altitude and projected planner position concurrently and resolves the local minima problem if occurred. On the other hand, many classical models in dynamic environments require several additional inputs, such as the relative position and relative velocity, which increase the requirement on the measurement system to localize the moving objects in the 3D Space. Several experiments were performed and discussed to verify the robustness and effectiveness of the proposed motion planner with real-time implementations. The system performance was validated using three robotics platforms, two quadcopter drones, and one ground robot. The position and orientation of each robot were defined using a motion capture system with 6 opti-track cameras. The motion planning system produces a quadcopter drone's efficient and accurate low-frequency trajectory. The generated trajectory allows the drone to track the ground robot and avoid collision effectively with the second drone in the vicinity.