Given a demonstration, a robot should be able to generalize a skill to any object it encounters-but existing approaches to skill transfer often fail to adapt to objects with unfamiliar shapes. Motivated by examples of improved transfer from compositional modeling, we propose a method for improving transfer by decomposing objects into their constituent semantic parts. We leverage data-efficient generative shape models to accurately transfer interaction points from the parts of a demonstration object to a novel object. We autonomously construct an objective to optimize the alignment of those points on skill-relevant object parts. Our method generalizes to a wider range of object geometries than existing work, and achieves successful one-shot transfer for a range of skills and objects from a single demonstration, in both simulated and real environments.
Cross-task generalization is a core challenge in open-world robotic manipulation, and the key lies in extracting transferable manipulation knowledge from seen tasks. Recent in-context learning approaches leverage seen task demonstrations to generate actions for unseen tasks without parameter updates. However, existing methods provide only low-level continuous action sequences as context, failing to capture composable skill knowledge and causing models to degenerate into superficial trajectory imitation. We propose Decompose and Recompose, a skill reasoning framework using atomic skill-action pairs as intermediate representations. Our approach decomposes seen demonstrations into interpretable skill--action alignments, enabling the model to recompose these skills for unseen tasks through compositional reasoning. Specifically, we construct a task-adaptive dynamic demonstration library via visual-semantic retrieval combined with skill sequences from a planning agent, complemented by a coverage-aware static library to fill missing skill patterns. Together, these yield skill-comprehensive demonstrations that explicitly elicit compositional reasoning for skill composition and execution ordering. Experiments on the AGNOSTOS benchmark and real-world environments validate our method's zero-shot cross-task generalization capability.
Generalizing robotic manipulation to unseen objects remains challenging, as learning-based approaches require many demonstrations and fail in few-shot settings. Prior work transfers affordances through semantic retrieval, but semantics alone neglect geometric similarity, which is critical for manipulation. We propose GRAFT, a geometry-aware correspondence framework for zero-shot manipulation transfer using only one demonstration per object. Objects are represented as part-based graphs, where part-level descriptors support global instance retrieval and part correspondence, and vertex-level descriptors enable fine-grained contact point matching. For an unseen object, our method first retrieves the most functionally and geometrically similar instance from the demonstration buffer with aligned functional parts, and finally propagates the contact points through point-wise correspondence.
Transferring manipulation skills across object instances that share functionality but differ in geometry remains a fundamental challenge in robot learning. While recent correspondence methods leverage dense visual descriptors and 3D feature fields, nearest-neighbor feature matching often produces spatially incoherent correspondences that fail to recover the local geometric frames required for reliable skill transfer. We introduce SemAnCorr, a training-free framework that establishes dense correspondence by selecting semantically consistent anchor regions through joint pose-correspondence optimization and propagating these constraints over the object surface using functional maps. The resulting correspondences preserve both semantic consistency and geometric coherence, enabling object-centric manipulation skills to transfer across geometrically diverse instances. We evaluate SemAnCorr on a dense correspondence benchmark built on PartNet-Mobility, achieving 90.8% semantic accuracy in our benchmark evaluation while improving geometric coherence over recent state-of-the-art baselines. Finally, we show that these improvements translate directly into real-world manipulation performance: using a single demonstration, SemAnCorr enables substantially more reliable zero-shot manipulation skill transfer to previously unseen objects than existing correspondence methods. Videos and additional visualizations are available at https://semancorr.github.io .