This study presents a novel obstacle evasion method for unmanned aerial vehicle (UAV) clusters in the presence of static and dynamic obstacles. First, a discrete three-dimensional model of the UAV is provided. Second, the proposed improved artificial potential field (APF) is illustrated. In designing the improved scheme, a pseudo-exponential function is fused into the potential field, thus avoiding local extreme points. Frictional resistance is introduced to optimize vibration and maintain stability after reaching the desired endpoints. Meanwhile, the relevant parameters are optimized, and appropriate state limits are defined, thus enhancing the control stability. Third, Lyapunov stability analysis proves that all signals in the closed-loop cluster system are ultimately bounded. Finally, the simulation results demonstrate that the UAV cluster can efficiently reconstruct, form, and maintain formations while avoiding static and dynamical obstacles along with maintaining a safe distance, solving the problem of the local extreme of traditional artificial potential field methods. The proposed scheme is also tested under large-scale multi-UAV scenarios. In conclusion, this study provides valuable insights for engineers working with UAV clusters navigating through formations.