RelAfford6D: Relational 6D Affordance Graphs for Constraint-Driven Robotic Manipulation

Bridging abstract semantics and precise physical control re-mains a fundamental challenge in open-world robotic manipulation. Whilerecent data-driven policies show promise, their reliance on isolated con-tact points or latent affordance embeddings lacks the rigorous kinematicconstraints necessary for complex articulated objects.To overcome thelimitation, we introduce RelAfford6D, a novel training-free frameworkcentered on a Relational 6D Affordance Graph. Given a free-form in-struction, our system deduces a semantic topology linking a primary in-teracting part to its physical anchor. By elevating these topological nodesinto precise metric SE(3) poses via vision foundation models, we analyti-cally formulate downstream execution as a kinematic constraint satisfac-tion problem. The robot synthesizes continuous trajectories by trackingstrictly defined physical manifolds (e.g., revolute or prismatic orbits).Coupled with a closed-loop tracking mechanism for dynamic replanningagainst disturbances, our physically grounded approach achieves supe-rior zero-shot success rates, cross-category generalization and executionrobustness in both simulation and the real world environments, outper-forming existing data-driven baselines.