The idea of creating collective aerial systems is appealing because several rather simple flying vehicles could join forces to cover a large area in little time in applications such as monitoring, mapping, search and rescue, or airborne communication relays. In most of these scenarios, a fleet of cooperating vehicles is dispatched to a confined airspace area and requested to fly close to a nominal altitude. Moreover, depending on the task each vehicle is assigned to, individual flight trajectories in this essentially two-dimensional space may interfere, resulting in disastrous collisions. This paper begins by introducing a probabilistic model to predict the rate of midair collisions that would occur if nothing is done to prevent them. In a second step, a control strategy for midair collision avoidance is proposed, which is interesting because it requires only local communication and information about flight altitudes. The proposed strategy is systematically analyzed ill theory and simulation as well as in experiments with five physical aerial vehicles. A significant reduction in collision rates can be achieved. Statistically, values close to zero are possible when the swarm's density is below an application-dependent threshold. Such low collision rates warrant an acceptable level of confidence in collision-free operation of a physical swarm. (C) 2011 Wiley Periodicals, Inc.