DiffMorphGrasp: A Diffusion Framework Conditioned on Hand Morphology for Cross-Embodiment Grasp Generation

Cross-embodiment dexterous grasp generation remains challenging because robotic hands differ substantially in geometry, topology, and kinematics. Existing approaches often lack explicit correspondences between structurally different hand regions that play similar functional roles in a grasp, a concept we refer to as functional correspondence. Consequently, their models tend to learn hand-specific interaction patterns rather than transferable grasp knowledge, limiting generalization to unseen hands. To address this limitation, we introduce FunCo-Grasp, which establishes functional correspondences across heterogeneous hand embodiments. Specifically, Functional Part Alignment aligns each hand to a canonical functional schema by mapping physical links to shared functional parts according to their grasping roles, while Canonical Frame Alignment expresses these parts in canonical local frames. These two alignments provide a consistent representation for inter-part and hand-object interactions, allowing the model to learn transferable grasp knowledge across hands. Conditioned on the aligned hand representation and object geometry, a diffusion model generates the target spatial arrangement of the functional parts, which are then converted into an executable joint configuration. Adapting FunCo-Grasp to an unseen hand requires only its geometric and kinematic models and a one-time lightweight functional annotation, without target-hand grasp data, fine-tuning, or learned retargeting. In simulation on held-out objects from the filtered CMapDataset, we achieves average success rates of 92.40% on three seen hands and 74.02% on four unseen hands. In real-world experiments, the same model achieves an overall success rate of 76.00% on two unseen hands without additional training or fine-tuning. These results demonstrate the effectiveness of FunCo-Grasp in transferring grasp knowledge to unseen hands.

To meet the demands of increasingly diverse dexterous hand hardware, it is crucial to develop a policy that enables zero-shot cross-embodiment grasping without redundant re-learning. Cross-embodiment alignment is challenging due to heterogeneous hand kinematics and physical constraints. Existing approaches typically predict intermediate motion targets and retarget them to each embodiment, which may introduce errors and violate embodiment-specific limits, hindering transfer across diverse hands. To overcome these limitations, we propose DexGrasp-Zero, a policy that learns universal grasping skills from diverse embodiments, enabling zero-shot transfer to unseen hands. We first introduce a morphology-aligned graph representation that maps each hand's kinematic keypoints to anatomically grounded nodes and equips each node with tri-axial orthogonal motion primitives, enabling structural and semantic alignment across different morphologies. Relying on this graph-based representation, we design a Morphology-Aligned Graph Convolutional Network (MAGCN) to encode the graph for policy learning. MAGCN incorporates a Physical Property Injection mechanism that fuses hand-specific physical constraints into the graph features, enabling adaptive compensation for varying link lengths and actuation limits for precise and stable grasping. Our extensive simulation evaluations on the YCB dataset demonstrate that our policy, jointly trained on four heterogeneous hands (Allegro, Shadow, Schunk, Ability), achieves an 85% zero-shot success rate on unseen hardware (LEAP, Inspire), outperforming the state-of-the-art method by 59.5%. Real-world experiments further evaluate our policy on three robot platforms (LEAP, Inspire, Revo2), achieving an 82% average success rate on unseen objects.

Dexterous grasp generation across robot hands is challenging because hands differ in kinematic topology, actuation dimensions, and native command spaces. We introduce GraspGraphNet, a topology-aware grasp generation framework that represents each hand as a URDF-derived kinematic graph and directly generates executable palm poses and joint configurations. GraspGraphNet combines hierarchical object surface encoding, differentiable forward kinematics, and dynamic world-edge message passing to model evolving robot-object interactions. It applies conditional flow matching directly in executable palm-pose and joint-state space, avoiding post-processing optimization, inverse kinematics, and retargeting. Using a shared model trained on Barrett Hand, Allegro Hand, and Shadow Hand, GraspGraphNet achieves an average success rate of 83.48% with 40ms inference time per grasp on a 40-object benchmark. Without retraining, the same model achieves 72.70% success on controlled finger-removal variants, demonstrating robustness to hand-topology variations. These results suggest that graph-structured hand representations can effectively support dexterous grasp generation across robot hands with different kinematic structures. Project: https://lysees.github.io/graspgraphnet-page