To address the formation control issue of multiple unmanned aerial vehicles (UAVs), a finite-time control scheme based on terminal sliding mode (TSM) is investigated in this paper. A quadcopter UAV with the vertical takeoff property is considered, with cascaded kinematics composed of rotational and translational loops. To strengthen the application in the low-cost UAV system, the applied torque is synthesized with an auxiliary rotational system, which can avoid utilizing direct attitude measurement. Furthermore, a terminal sliding mode surface is established and employed in the finite-time formation control protocol (FTFCP) as the driven thrust of multiple UAVs over an undirected topology in the translational system. To maintain the safe flight of the UAV clusters in an environment to avoid collision with obstacles or with other UAV neighbors, a pigeon-hierarchy-inspired obstacle avoidance protocol (PHOAP) is proposed. By imitating the interactive hierarchy that exists among the homing pigeon flocks, the collision avoidance scheme is separately enhanced to generate the repulsive potential field for the leader maneuver target and the follower UAV cluster. Subsequently, the collision avoidance laws based on pigeon homing behavior are combined with the finite-time sliding mode formation protocol, and the applied torque is attached as a cascaded structure in the attitude loop to synthesize an obstacle avoidance cooperative control framework. Finally, simulation scenarios of multiple UAVs to reach a desired formation among obstacles is investigated, and the effectiveness of the proposed approach is validated.