  Recently, there has been immense interest in using unmanned aerial vehicles
(UAVs) for civilian operations such as package delivery, firefighting, and fast
disaster response. As a result, UAV traffic management systems are needed to
support potentially thousands of UAVs flying simultaneously in the airspace, in
order to ensure their liveness and safety requirements are met. Hamilton-Jacobi
(HJ) reachability is a powerful framework for providing conditions under which
these requirements can be met, and for synthesizing the optimal controller for
meeting them. However, due to the curse of dimensionality, HJ reachability is
only tractable for a small number of vehicles if their set of maneuvers is
unrestricted. In this paper, we define a platoon to be a group of UAVs in a
single-file formation. We model each vehicle as a hybrid system with modes
corresponding to its role in the platoon, and specify the set of allowed
maneuvers in each mode to make the analysis tractable. We propose several
liveness controllers based on HJ reachability, and wrap a safety controller,
also based on HJ reachability, around the liveness controllers. For a single
altitude range, our approach guarantees safety for one safety breach; in the
unlikely event of multiple safety breaches, safety can be guaranteed over
multiple altitude ranges. We demonstrate the satisfaction of liveness and
safety requirements through simulations of three common scenarios.
