This paper introduces a novel multi-leader hierarchical control architecture based on the Reynolds model for UAV swarms. By employing hierarchical graph distances, the system partitions each leader along with its surrounding followers, effectively decomposing the swarm into several localized neighborhood clusters. The interactions among multiple leaders in an obstacle-free environment are meticulously designed, and the efficacy of the swarm's collision avoidance control is tested when dynamic obstacles are introduced. The study further delves into the control interactions between leaders and followers within these local neighborhood clusters. Extensive simulation results underscore that the swarm maintains stability and achieves convergence in both inter-drone collision avoidance and evasion of external dynamic obstacles. This comprehensive approach not only enhances collision avoidance control of UAV swarms amidst dynamic obstacles but also addresses critical formation control challenges encountered during the avoidance process. The findings from this research hold significant implications for the development of more efficient and reliable UAV swarm control systems in dynamic and unpredictable environments.