  In this paper, we present Neural-Swarm, a nonlinear decentralized stable
controller for close-proximity flight of multirotor swarms. Close-proximity
control is challenging due to the complex aerodynamic interaction effects
between multirotors, such as downwash from higher vehicles to lower ones.
Conventional methods often fail to properly capture these interaction effects,
resulting in controllers that must maintain large safety distances between
vehicles, and thus are not capable of close-proximity flight. Our approach
combines a nominal dynamics model with a regularized permutation-invariant Deep
Neural Network (DNN) that accurately learns the high-order multi-vehicle
interactions. We design a stable nonlinear tracking controller using the
learned model. Experimental results demonstrate that the proposed controller
significantly outperforms a baseline nonlinear tracking controller with up to
four times smaller worst-case height tracking errors. We also empirically
demonstrate the ability of our learned model to generalize to larger swarm
sizes.
