  We present Neural-Swarm2, a learning-based method for motion planning and
control that allows heterogeneous multirotors in a swarm to safely fly in close
proximity. Such operation for drones is challenging due to complex aerodynamic
interaction forces, such as downwash generated by nearby drones and ground
effect. Conventional planning and control methods neglect capturing these
interaction forces, resulting in sparse swarm configuration during flight. Our
approach combines a physics-based nominal dynamics model with learned Deep
Neural Networks (DNNs) with strong Lipschitz properties. We make use of two
techniques to accurately predict the aerodynamic interactions between
heterogeneous multirotors: i) spectral normalization for stability and
generalization guarantees of unseen data and ii) heterogeneous deep sets for
supporting any number of heterogeneous neighbors in a permutation-invariant
manner without reducing expressiveness. The learned residual dynamics benefit
both the proposed interaction-aware multi-robot motion planning and the
nonlinear tracking control design because the learned interaction forces reduce
the modelling errors. Experimental results demonstrate that Neural-Swarm2 is
able to generalize to larger swarms beyond training cases and significantly
outperforms a baseline nonlinear tracking controller with up to three times
reduction in worst-case tracking errors.
