In this paper, the 3D leader–follower formation control problem, which focuses on swarms of fixed-wing Unmanned Aerial Vehicles (UAVs) with motion constraints and disturbances, has been investigated. Original formation errors of the follower UAVs have been transformed into the Frenet-Serret frame. Formation control laws satisfying five motion constraints (i.e., linear veloc-ity, linear acceleration, heading rate, climb rate and climb angle) have been designed. The conver-gence of the control laws has been discussed via the Lyapunov stability tool. In addition, to address the unknown disturbances, an adaptive disturbance observer is exploited. Furthermore, formation control laws involving estimated disturbances are presented as well. The collision avoidance between UAVs is achieved with the artificial potential method. Simulation results obtained using four scenarios verify the effectiveness of the proposed method in situations with constant distur-bances and varying disturbances, as well as without disturbances.