This paper considers the problem of controlling a formation of quadrotor UAVs equipped with onboard cameras able to measure relative bearings in their local body frames w.r.t. neighboring UAVs. The control goal is twofold: (i) steering the agent group towards a formation defined in terms of desired bearings, and (ii) actuating the group motions in the ‘null-space’ of the current bearing formation. The proposed control strategy relies on an extension of the rigidity theory to the case of directed bearing frameworks in R 3×S1 . This extension allows to devise a decentralized bearing controller which, unlike most of the present literature, does not need presence of a common reference frame or of reciprocal bearing measurements for the agents. Simulation and experimental results are then presented for illustrating and validating the approach.