We present a distributed control strategy for a team of agents to autonomously achieve a desired 3D formation. Our approach is based on local relative position measurements and can be applied to multirotor aerial vehicles. We assume that agents have a common sense of direction, which is used to align the z-axes of their local coordinate frames. However, this assumption is not crucial, and our approach is provably robust to misalignments in the local coordinate frames or measurement inaccuracies. In particular, agents can move along any direction that projects positively onto the desired direction of motion. This property is exploited to design a fully-distributed collision avoidance strategy. We validate the proposed approach experimentally and show that a team of quadrotors can achieve a desired 3D formation without collisions.