This paper addresses the problem of formation control of multiple quadrotor vehicles, focusing on ensuring inter-vehicle collision avoidance in the presence of time-varying external disturbances. The problem is divided into two sub-problems: (i) the generation of collision-free trajectories; and (ii) trajectory tracking. Initially, by employing the Lyapunov-based backstepping technique, a set of collision-free trajectories is generated based on a potential function. Additionally, a trajectory tracking controller is developed for each individual quadrotor, ensuring accurate tracking of their respective trajectories. Furthermore, to attain robust tracking performance, nonlinear disturbance observers are developed and incorporated into the control inputs to compensate for time-varying external disturbances. Comprehensive simulation and experimental results are provided and analyzed to demonstrate the effectiveness and performance of the proposed strategy.