Deep neural networks for graphs have emerged as a powerful tool for learning on complex non-euclidean data, which is becoming increasingly common for a variety of different applications. Yet, although their potential has been widely recognised in the machine learning community, graph learning is largely unexplored for downstream tasks such as robotics applications. To fully unlock their potential, hence, we propose a review of graph neural architectures from a robotics perspective. The paper covers the fundamentals of graph-based models, including their architecture, training procedures, and applications. It also discusses recent advancements and challenges that arise in applied settings, related for example to the integration of perception, decision-making, and control. Finally, the paper provides an extensive review of various robotic applications that benefit from learning on graph structures, such as bodies and contacts modelling, robotic manipulation, action recognition, fleet motion planning, and many more. This survey aims to provide readers with a thorough understanding of the capabilities and limitations of graph neural architectures in robotics, and to highlight potential avenues for future research.

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