Imitation learning (IL) can train computationally-efficient sensorimotor policies from a resource-intensive Model Predictive Controller (MPC), but it often requires many samples, leading to long training times or limited robustness. To address these issues, we combine IL with a variant of robust MPC that accounts for process and sensing uncertainties, and we design a data augmentation (DA) strategy that enables efficient learning of vision-based policies. The proposed DA method, named Tube-NeRF, leverages Neural Radiance Fields (NeRFs) to generate novel synthetic images, and uses properties of the robust MPC (the tube) to select relevant views and to efficiently compute the corresponding actions. We tailor our approach to the task of localization and trajectory tracking on a multirotor, by learning a visuomotor policy that generates control actions using images from the onboard camera as only source of horizontal position. Numerical evaluations show 80-fold increase in demonstration efficiency and a 50% reduction in training time over current IL methods. Additionally, our policies successfully transfer to a real multirotor, achieving low tracking errors despite large disturbances, with an onboard inference time of only 1.5 ms. Video: https://youtu.be/_W5z33ZK1m4
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