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

Affordance-guided imitation learning has shown impressive performance in robotic manipulation tasks by compressing visual perception into task-specific geometric constraints (e.g., fixed contact points). However, the commonly used static affordances can become inconsistent in precision-critical tasks or under object location perturbations, leading to post-contact trajectory drift. To address this issue, we propose AffordTrajDP, a dynamic framework that constructs affordance trajectories via object-centric temporal propagation to guide the progressive manipulation process. Specifically, given an RGB-D observation, our core insight is that a retrieved anchor affordance, which captures the desired contact point between the end-effector and the target object, can be propagated forward via affordance propagation, using the object's SE(3) pose as a natural propagation medium, to yield an affordance trajectory that provides temporally consistent, state-aware guidance throughout execution. AffordTrajDP achieves 70.0% average success rate on ManiSkill3, outperforming strong baselines by up to 17.8%. Real-world experiments on Galaxea A1 and UR7e robotic arms, covering StackCube, PickCup, AdapterInsertion, Ring-on-Peg, Put-in-Bowl, and USB Insertion, further validate robustness under object placement variations and appearance changes, with seen and unseen object instances evaluated on Galaxea A1, and ablations confirm the contribution of each proposed component.

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.

Learning manipulation skills from human videos is promising for scalable robot learning. However, the embodiment mismatch between humans and robots makes this challenging. One promising solution is to learn object-centric actionable affordances that are embodiment-agnostic. In this work, we propose a framework that leverages egocentric human videos with state-of-the-art 3D Structure-from-Motion and hand mesh reconstruction to extract actionable affordances such as visual, grasp, and trajectory affordances that explicitly encode where to interact, how to grasp, and how to move. We construct EgoAffordance, a large-scale dataset comprising 204K episodes with 5.6M visual affordances and 11.6M grasp and trajectory affordances. Building on this, we introduce VLAff, a large vision-language model-based unified foundation model that learns cross-modal correlations across all actionable affordances. Given a visual observation and instruction, VLAff generates visual affordance heatmaps, grasp poses, and trajectories, which are then converted into directly executable actions by utilizing 3D scene information. Through extensive experiments, we demonstrate that VLAff not only achieves state-of-the-art performance on visual affordance prediction, but can also be effectively applied to real robot applications such as zero-shot manipulation and affordance-guided robot learning.