This paper presents a novel method for controlling swarms of unmanned aerial vehicles using Stochastic Optimal Control (SOC) theory. The approach consists of a centralized high-level controller that computes optimal state trajectories as velocity sequences, and a platform-specific low-level controller which ensures that these velocity sequences are met. The high-level control task is expressed as a centralized Path Integral control problem, for which optimal control computation corresponds to a probabilistic inference problem that can be solved by efficient sampling methods. Through simulation we show that our SOC approach (a) has significant benefits compared to deterministic control and other SOC methods in multi-modal problems with noise-dependent optimal solutions, (b) is capable of controlling a large number of platforms in real-time, and (c) yields collective emergent behavior in the form of flight formations. Finally, we show that our approach works for real platforms, by controlling a swarm of three quadrotors

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