  Imitation Learning (IL) can generate computationally efficient policies from
demonstrations provided by Model Predictive Control (MPC). However, IL methods
often require extensive data-collection and training efforts, limiting changes
to the policy if the task changes, and they produce policies with limited
robustness to new disturbances. In this work, we propose an IL strategy to
efficiently compress a computationally expensive MPC into a deep neural network
policy that is robust to previously unseen disturbances. By using a robust
variant of the MPC, called Robust Tube MPC, and leveraging properties from the
controller, we introduce computationally efficient data augmentation methods
that enable a significant reduction of the number of MPC demonstrations and
training efforts required to generate a robust policy. Our approach opens the
possibility of zero-shot transfer of a policy trained from a single MPC
demonstration collected in a nominal domain, such as a simulation or a robot in
a lab/controlled environment, to a new domain with previously unseen bounded
model errors/perturbations. Numerical evaluations performed using linear and
nonlinear MPC for agile flight on a multirotor show that our method outperforms
strategies commonly employed in IL (such as Dataset-Aggregation (DAgger) and
Domain Randomization (DR)) in terms of demonstration-efficiency, training time,
and robustness to perturbations unseen during training. Experimental
evaluations validate the efficiency and real-world robustness.
