Not yet reviewed by Pith; the record is open.

Grounding object affordance is fundamental to robotic manipulation as it establishes the critical link between perception and action among interacting objects. However, prior works predominantly focus on predicting single-object affordance, overlooking the fact that most real-world interactions involve relationships between pairs of objects. In this work, we address the challenge of object-to-object affordance grounding under limited data contraints. Inspired by recent advances in few-shot learning with 2D vision foundation models, we propose a novel one-shot 3D object-to-object affordance learning approach for robotic manipulation. Semantic features from vision foundation models combined with point cloud representation for geometric understanding enable our one-shot learning pipeline to generalize effectively to novel objects and categories. We further integrate our 3D affordance representation with large language models (LLMs) for robotics manipulation, significantly enhancing LLMs' capability to comprehend and reason about object interactions when generating task-specific constraint functions. Our experiments on 3D object-to-object affordance grounding and robotic manipulation demonstrate that our O$^3$Afford significantly outperforms existing baselines in terms of both accuracy and generalization capability.