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Abstract In this work, we propose a novel adaptive formation control architecture for a group of quadrotor systems, under line‐of‐sight (LOS) distance and relative distance constraints as well as attitude constraints, where the constraint requirements can be both asymmetric and time‐varying in nature. The LOS distance constraint consideration ensures that each quadrotor is not deviating too far away from its desired flight trajectory. The LOS relative inter‐quadrotor distance constraint is to guarantee that the LOS distance between any two quadrotors in the formation is neither too large (which may result in the loss of communication between quadrotors, for example) nor too small (which may result in collision between quadrotors, for example). The attitude constraints make sure that the roll, pitch, and yaw angles of each quadrotor do not deviate too much from the desired profile. Universal barrier functions are adopted in the controller design and analysis, which is a generic framework that can address system with different types of constraints in a unified controller architecture. Furthermore, each quadrotor's mass and inertia are unknown, and the system dynamics are subjected to time‐varying external disturbances. Through rigorous analysis, an exponential convergence rate can be guaranteed on the distance and attitude tracking errors, while all constraints are satisfied during the operation. A simulation example further demonstrates the efficacy of the proposed control framework.