We study the problem of hanging a wide range of grasped objects on diverse supporting items. Hanging objects is a ubiquitous task that is encountered in numerous aspects of our everyday lives. However, both the objects and supporting items can exhibit substantial variations in their shapes and structures, bringing two challenging issues: (1) determining the task-relevant geometric structures across different objects and supporting items, and (2) identifying a robust action sequence to accommodate the shape variations of supporting items. To this end, we propose Semantic Keypoint Trajectory (SKT), an object-agnostic representation that is highly versatile and applicable to various everyday objects. We also propose Shape-conditioned Trajectory Deformation Network (SCTDN), a model that learns to generate SKT by deforming a template trajectory based on the task-relevant geometric structure features of the supporting items. We conduct extensive experiments and demonstrate substantial improvements in our framework over existing robot hanging methods in the success rate and inference time. Finally, our simulation-trained framework shows promising hanging results in the real world. For videos and supplementary materials, please visit our project webpage: https://hcis-lab.github.io/SKT-Hang/.

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