Sub-\SI{50}{\gram} nano-drones are gaining momentum in both academia and industry. Their most compelling applications rely on onboard deep learning models for perception despite severe hardware constraints (\ie sub-\SI{100}{\milli\watt} processor). When deployed in unknown environments not represented in the training data, these models often underperform due to domain shift. To cope with this fundamental problem, we propose, for the first time, on-device learning aboard nano-drones, where the first part of the in-field mission is dedicated to self-supervised fine-tuning of a pre-trained convolutional neural network (CNN). Leveraging a real-world vision-based regression task, we thoroughly explore performance-cost trade-offs of the fine-tuning phase along three axes: \textit{i}) dataset size (more data increases the regression performance but requires more memory and longer computation); \textit{ii}) methodologies (\eg fine-tuning all model parameters vs. only a subset); and \textit{iii}) self-supervision strategy. Our approach demonstrates an improvement in mean absolute error up to 30\% compared to the pre-trained baseline, requiring only \SI{22}{\second} fine-tuning on an ultra-low-power GWT GAP9 System-on-Chip. Addressing the domain shift problem via on-device learning aboard nano-drones not only marks a novel result for hardware-limited robots but lays the ground for more general advancements for the entire robotics community.
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