Affine formation control can generate and transform the overall formation by only using the configurations of a few key nodes， featuring high flexibility and good scalability. For the affine formation control problem of fixed-wing UAV swarms， an affine formation hierarchical control scheme is designed， incorporating leader cooperative path following， follower tracking， and collision avoidance. This scheme divides the swarm into a leader layer and a follower layer： multiple leaders cooperatively generate the reference configuration required for the swarm formation while following the preset path， followers only need to track the desired positions in the affine formation spanned by the leader positions. Meanwhile， collision avoidance control ensures that each UAV avoids environmental obstacles and prevents inter-UAV collisions. Compared with existing algorithms， this method achieves a higher obstacle avoidance success rate， guarantees inter-UAV safety， and enables faster convergence of follower tracking error. Furthermore， a software-in-the-loop simulation of six UAVs is completed on the XTDrone platform built based on ROS and Gazebo. In the simulation， UAVs can form the desired affine formation and fly safely without collisions throughout the process. The relevant codes have been-released as open source.