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There are many examples in nature where large groups of individuals are able to maintain 3-D formations while navigating in complex environments. This paper addresses the development of a framework and robot controllers that enable a group of aerial robots to maintain a formation with partial state information while avoiding collisions. The central concept is to develop a low-dimensional abstraction of the large teams of robots, facilitate planning, command, and control in a low-dimensional space, and to realize commands or plans in the abstract space by synthesizing controllers for individual robots that respect the specified abstraction. We derive the basic theory and present experimental and simulation results with a team of rotor crafts.