GRAFT: Graph-Based Affordance Transfer via Part 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 .

Bridging abstract semantics and precise physical control remains a fundamental challenge in open-world robotic manipulation. While recent data-driven policies show promise, their reliance on isolated contact points or latent affordance embeddings lacks the rigorous kinematic constraints necessary for complex articulated objects.To overcome the limitation, we introduce RelAfford6D, a novel training-free framework centered on a Relational 6D Affordance Graph. Given a free-form instruction, our system deduces a semantic topology linking a primary interacting part to its physical anchor. By elevating these topological nodes into precise metric $SE(3)$ poses via vision foundation models, we analytically formulate downstream execution as a kinematic constraint satisfaction problem. The robot synthesizes continuous trajectories by tracking strictly defined physical manifolds (e.g., revolute or prismatic orbits). Coupled with a closed-loop tracking mechanism for dynamic replanning against disturbances, our physically grounded approach achieves superior zero-shot success rates, cross-category generalization and execution robustness in both simulation and the real world environments, outperforming existing data-driven baselines.

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.