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Function beyond Form: Functional Correspondence for Cross-Embodiment Dexterous Grasp Generation

Bolin Zou, Wenlong Dong, Mu Ai, Chao Tang, Aoxiang Gu, Lipeng Chen, Hong Zhang

arXiv:2609.39006v1cs.RO

TL;DR

Cross-embodiment grasp generation is challenged by hand diversity and missing functional correspondences between regions with similar grasping roles. FunCo-Grasp aligns functional parts and their canonical frames, then generates grasps from the aligned hand and object geometry. It reports transfer to unseen hands in simulation and real-world experiments.

  • Problem

    Existing approaches lack explicit correspondences between structurally different hand regions with similar grasp roles, and their interaction patterns remain hand-specific, limiting transfer to unseen hands.

    Source: §I · p. 1

  • Method

    FunCo-Grasp maps physical links to shared functional parts in canonical local frames, then uses a diffusion model conditioned on the aligned hand and object geometry to generate part arrangements for conversion into joint configurations.

    Source: §I · p. 2, B. Cross-Embodiment Functional… · p. 3, D. Functional-Part-Based Grasp… · p. 5

  • Results

    92.40% average grasp success on three seen hands and 74.02% on four unseen hands in simulation, plus 76.00% overall on two unseen hands in real-world experiments.

    Source: §I · p. 2

  • Takeaways & Limitations

    Adapting to an unseen hand requires its geometric and kinematic models and a one-time lightweight functional annotation, without target-hand grasp data, fine-tuning, or learned retargeting.

    Source: §I · p. 2

    Grasp diversity remains below the paper-reported baseline values, motivating future work on task-conditioned generation guided by human demonstrations.

    Source: §V · p. 8

Abstract

from arXiv · show

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.

I. INTRODUCTION

Cross-embodiment grasp generation is difficult because hands vary in morphology and kinematics, while existing interaction representations lack functional correspondences between structurally different regions. FUNCO-GRASP aligns hands through shared functional parts and canonical frames, and reports successful transfer to unseen hands in simulation and real-world experiments.

I. INTRODUCTION

  • Hand morphology and kinematic diversity, combined with missing functional correspondences, make grasp knowledge difficult to transfer to unseen hands.Existing interaction-centric methods use hand-specific points, links, or local frames, so they tend to learn hand-specific interaction patterns.Source: §I · p. 1
  • FUNCO-GRASP maps physical links to shared functional parts by grasping role, expresses them in canonical local frames, and uses a diffusion model to generate functional-part arrangements.The generated arrangement is converted into executable joint configurations; adapting to an unseen hand requires its geometric and kinematic models and a one-time lightweight functional annotation, not target-hand grasp data, fine-tuning, or learned retargeting.Source: §I · p. 2
  • FUNCO-GRASP achieves 92.40% average grasp success on three seen hands and 74.02% on four unseen hands in simulation, plus 76.00% overall on two unseen hands in real-world experiments.The simulation evaluation uses held-out objects from the filtered CMapDataset; real-world tests use the same model without additional training or fine-tuning.Source: §I · p. 2
  • The proposed functional-part-based representation establishes correspondences for inter-part and hand-object interactions across hands.The framework is proposed for cross-embodiment dexterous grasp generation across heterogeneous hands.Source: §I · p. 2

II. RELATED WORK

Prior grasp representations differ in whether they encode hand states, object contacts, or hand-object relations, while morphology-aware transfer methods chiefly align articulations or control spaces. FUNCO-GRASP instead aligns functional regions for interactions across hands.

A. Dexterous Grasp Representation

  • Hand-centric methods directly encode hand-specific poses or configurations, while object-centric methods predict surface contacts without explicitly modeling the coordinated hand configuration needed for a stable grasp.Matching predicted contacts alone does not guarantee kinematic feasibility, collision-free finger placement, or favorable grasp geometry.Source: A. Dexterous Grasp Representation · p. 2
  • Interaction-centric methods model hand-object spatial relations, but hand-specific samples, links, and frames can have ambiguous correspondences across different hands.FUNCO-GRASP maps physical links to shared functional parts to represent inter-part and hand-object interactions and transfer grasp knowledge without target-hand grasp data, fine-tuning, or learned retargeting.Source: A. Dexterous Grasp Representation · p. 2

B. Morphology-Aware Cross-Embodiment Learning

  • Prior morphology-aware methods organize joint articulations, control commands, or canonical pose spaces; FUNCO-GRASP aligns functional parts for inter-part and hand-object interactions.A functional part may include multiple physical links and is expressed in a canonical local frame.Source: B. Morphology-Aware Cross-Embodiment… · p. 2

III. METHOD

The method represents cross-embodiment grasps through functional correspondences, encodes the hand and object, and generates functional-part arrangements. Its problem formulation takes an object point cloud and a target hand model with a one-time functional annotation to produce an executable grasp.

III. METHOD

  • FUNCO-GRASP has three stages: cross-embodiment functional correspondence, hand and object encoding, and functional-part-based grasp generation.The generation stage conditions on the aligned hand representation and object geometry to produce a spatial arrangement of functional parts, then converts it to executable joint configurations via inverse kinematics.Source: §III · p. 2, Figure 2 · p. 3

A. Problem Formulation

  • The target-hand problem takes an object point cloud, the hand's geometric and kinematic models, and a one-time lightweight functional annotation as inputs.The annotation and models support transfer without target-hand grasp data, fine-tuning, or learned retargeting.Source: A. Problem Formulation · p. 3
  • The output is an executable grasp with a wrist pose in the object frame and internal joint angles that should stably hold the object within kinematic constraints and joint limits.The internal angles exclude the wrist degrees of freedom.Source: A. Problem Formulation · p. 3

B. Cross-Embodiment Functional Correspondence

Functional-part and canonical-frame alignments establish cross-hand correspondences, while separate hand and object encoders provide conditions for grasp generation.

B. Cross-Embodiment Functional Correspondence

  • Functional Part Alignment maps physical links to shared functional parts by grasping role, while Canonical Frame Alignment expresses corresponding parts in canonical local frames.Functional parts may group multiple links, and absent parts may be omitted.Source: B. Cross-Embodiment Functional… · p. 3

C. Hand and Object Encoding

  • The hand graph represents functional parts as nodes and connects adjacent parts along the kinematic tree, encoding part geometry, roles, kinematics, reference poses, and graph distances.Node features combine part point-cloud features with URDF attributes and part labels.Source: C. Hand and Object Encoding · p. 4, Figure 3 · p. 4
  • A separate object branch combines frozen VQ-VAE local patch descriptors with patch centers and object scale; the hand and object conditions remain fixed during each sampling run.Source: C. Hand and Object Encoding · p. 4

D. Functional-Part-Based Grasp Generation

A diffusion model generates functional-part arrangements conditioned on the aligned hand and object geometry, then inverse kinematics converts them into executable joint configurations.

D. Functional-Part-Based Grasp Generation

  • Conditioned on the aligned hand and object geometry, diffusion generates functional-part poses, representing the wrist in the object frame and other parts as residuals from reference poses.Translations are normalized by object scale, with wrist translation also centered on the object; invalid and padded channels are masked.Source: D. Functional-Part-Based Grasp… · p. 4
  • Object–Node relations encode object patches in each part’s canonical frame, while Node–Node relations encode relative part poses; cross-attention and self-attention model these interactions.Source: D. Functional-Part-Based Grasp… · p. 4
  • Repeated stochastic DDIM updates transform Gaussian noise on valid channels into the generated part arrangement.Each update advances from timestep t to a sampled lower timestep t′.Source: D. Functional-Part-Based Grasp… · p. 4
  • Training predicts injected noise and uses penetration and contact losses to supervise the denoised part arrangement.The noise loss separately normalizes wrist and non-wrist translation and rotation blocks; geometric losses use the object signed distance field.Source: D. Functional-Part-Based Grasp… · p. 4
  • Table I reports grasp success on held-out objects and per-grasp runtime, marking the best and second-best values and identifying unavailable results.Source: Table I · p. 5
  • Figure 4 shows generated grasps on held-out objects for seen hands on the left and unseen hands on the right.The caption states that the same model transfers without target-hand grasp data, fine-tuning, or learned retargeting.Source: Figure 4 · p. 5
  • Inverse kinematics converts generated functional-part positions into executable joint configurations by fitting weighted part positions without explicitly matching their orientations.Adapting to an unseen hand requires its geometric and kinematic models and a one-time lightweight functional annotation, but no target-hand grasp data, fine-tuning, or learned retargeting.Source: D. Functional-Part-Based Grasp… · p. 5

IV. EXPERIMENTS

The evaluation covers simulation comparisons, alignment ablations, finger-length variations, diversity analysis, and real-world experiments.

  • The evaluation examines simulation comparisons, alignment ablations, finger-length variations, diversity, and real-world experiments to assess transfer to unseen hands.Source: §IV · p. 5

A. Experimental Setup

The experiments train on filtered CMapDataset grasps from three hands and test on held-out objects across seen and unseen hands. The setup also specifies baseline comparisons, evaluation procedures, implementation choices, and alignment and scaling visualizations.

A. Experimental Setup

  • Training uses 48 objects and 14,011 grasps from Allegro, Barrett, and ShadowHand; evaluation uses 10 held-out objects and four unseen hands.Adapting to each unseen hand requires its geometric and kinematic models plus a one-time lightweight functional annotation.Source: A. Experimental Setup · p. 5
  • The baselines include object-centric GenDexGrasp and CEDex, interaction-centric D(R, O) Grasp and T (R, O) Grasp, and UniMorphGrasp.The four released-checkpoint baselines retain their original settings; UniMorphGrasp results follow its published protocol, with unseen-hand results unavailable.Source: A. Experimental Setup · pp. 5–6
  • Fig. 5 depicts misplaced hand regions without FPA and disrupted coordinated closure without CFA; Fig. 6 plots success under finger-length scaling without retraining.In Fig. 6, 1.0× denotes original geometry.Source: Figure 5 · p. 6, Figure 6 · p. 6
  • Each hand–object pair receives three runs of 100 grasps, with success requiring final object displacement below 2 cm after six directional disturbances.Success is averaged over repetitions, objects, and hands; diversity is the standard deviation of successful configurations.Source: A. Experimental Setup · p. 6
  • The model has 13.647M parameters and uses 20-step stochastic DDIM with η = 1 and injected-noise scaling of 0.2.Results use the epoch-300 checkpoint; training runs for 300 epochs in FP32 on two RTX 5880 Ada GPUs.Source: A. Experimental Setup · p. 6

B. Simulation Results

FunCo-Grasp transfers to unseen hands while maintaining high seen-hand success and generating executable grasps efficiently. The evaluation also reports seen-hand grasp diversity and depicts real-world setups on two unseen hands.

B. Simulation Results

  • 92.40% average success on seen hands compares with 91.07% for T (R, O) Grasp and 85.33% for D(R, O) Grasp under local evaluation.FunCo-Grasp reaches 97.20% on Allegro and 93.80% on ShadowHand.Source: B. Simulation Results · p. 6
  • 74.02% average success on unseen hands exceeds CEDex at 66.50%, D(R, O) Grasp at 38.13%, and T (R, O) Grasp at 11.95%.FunCo-Grasp leads on three of four unseen hands, with gains over CEDex of 22.00, 10.73, and 8.90 percentage points on ApexHand, XHand, and LeapHand.Source: B. Simulation Results · p. 6
  • Table III reports diversity of successful grasps on seen hands in radians, with baseline values taken from their published protocols.UniMorphGrasp uses its full model.Source: Table III · p. 7
  • Fig. 7 shows Revo2 and ApexHand mounted on UR5 arms using RealSense D435i observations; both hands were unseen during training.The figure describes the real-world setups, not success rates.Source: Figure 7 · p. 7
  • 0.16 s per executable grasp, including inverse kinematics, compares with 0.21 s for T (R, O) Grasp, 0.75 s for D(R, O) Grasp, and 12.52 s for CEDex.This is a 23.81% runtime reduction versus T (R, O) Grasp and a 4.69× speedup over D(R, O) Grasp.Source: B. Simulation Results · p. 7

C. Ablation Studies

The ablations test Functional Part Alignment (FPA) and Canonical Frame Alignment (CFA) separately and together. Removing either sharply reduces unseen-hand success, while the ApexHand examples illustrate their complementary roles.

C. Ablation Studies

  • The variants replace functional parts with physical-link nodes without FPA, use native URDF axes without CFA, or combine both changes.All variants are trained from scratch with the same training data and optimization settings.Source: C. Ablation Studies · p. 7
  • Removing FPA or CFA reduces unseen-hand success from 74.02% to 33.90% or 19.40%, respectively; removing both reduces it to 0.95%.Seen-hand success remains between 90.13% and 90.73% across ablated variants, compared with 92.40% for the full model.Source: C. Ablation Studies · p. 7
  • On ApexHand, removing FPA yields misplaced hand regions and 13.40% success, while removing CFA disrupts coordinated closure and yields 10.40%.Together, shared functional parts and canonical local frames provide a consistent representation for inter-part and hand–object interactions.Source: C. Ablation Studies · p. 7

D. Robustness to Finger-Length Variations

The robustness evaluation scales finger lengths across all seven hands while keeping other specified geometry and kinematic properties fixed. Success remains high under increased finger lengths without retraining.

D. Robustness to Finger-Length Variations

  • Scaling changes finger links, fingertips, and downstream joint offsets along the forward axis from 0.8× to 1.2× while keeping palm and wrist geometry, topology, axes, limits, and canonical-frame orientations fixed.Geometry-dependent attributes are recomputed without retraining or redefining functional correspondence.Source: D. Robustness to Finger-Length… · p. 7
  • At 1.1× finger length, success exceeds 84% on all seen hands and reaches at least 63% on all unseen hands; at 1.2×, all remain above 75% and 60%, respectively.These evaluations require no retraining.Source: D. Robustness to Finger-Length… · p. 7

E. Diversity Analysis

The model achieves 76.00% overall success on two unseen hands in real-world experiments, while its grasp diversity remains below the reported baselines. The conclusion identifies task-conditioned generation guided by human demonstrations as future work.

E. Diversity Analysis

  • 0.293 rad diversity, below 0.401 rad for T (R, O) Grasp, 0.450 rad for D(R, O) Grasp, and 0.512 rad for CEDex.Limited variation is already present in the generated functional-part arrangements before inverse kinematics, suggesting grasp generation contributes at least partly.Source: E. Diversity Analysis · p. 7

F. Real-World Experiments

  • Real-world evaluation used UR5 arms with ApexHand or Revo2, testing each hand across ten random placements for each of 10 objects.A successful trial required lifting the object clear of the table and maintaining a stable grasp.Source: F. Real-World Experiments · pp. 7–8
  • 76.00% overall success on two unseen hands in real-world trials, with ApexHand at 84/100 and Revo2 at 68/100.The same model was used without additional training or fine-tuning.Source: F. Real-World Experiments · p. 8

V. CONCLUSION

  • The conclusion reports simulation transfer without target-hand grasp data, fine-tuning, or learned retargeting.It identifies task-conditioned grasp generation guided by human demonstrations as future work.Source: §V · p. 8
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