EquiGQNet: Fast Grasp Quality Evaluation via Shared Equivariant Point Cloud Encoding

I. INTRODUCTION

• For unseen objects in clutter, complex geometry can leave successful grasps in narrow regions, making accurate and efficient evaluation of diverse candidates important.The setting uses a point cloud from a single-view depth image.Source: §I · p. 1
• Scene-anchored methods may miss grasps between sampled locations and cannot directly evaluate arbitrary continuous 6-DoF candidates, while late fusion may lose local gripper-relative geometry.These limitations motivate evaluation of arbitrary candidates while retaining local geometry.Source: §I · pp. 1–2
• Early fusion captures object geometry relative to each grasp, but reconstructing inputs and rerunning the encoder for every candidate is computationally costly.The cost is especially relevant when evaluating many candidates or performing iterative optimization.Source: §I · p. 2
• EquiGQNet reuses one scene encoding: SO(3) equivariance supplies grasp-oriented features, while MAF adds grasp position before global aggregation to preserve local geometry.Together, these choices retain grasp-relative geometry without candidate-wise scene re-encoding.Source: §I · p. 2
• Experiments evaluate EquiGQNet in CEM-based continuous search and generative-planner candidate ranking, reporting reduced evaluation and planning time with strong performance on challenging unseen objects.The highlighted cases have complex geometry and limited graspable regions.Source: §I · p. 2

II. METHOD

• For each candidate, shared crop features are rotated to its grasp orientation and fused with its position through MAF before global aggregation.The grasp pose is represented by orientation R and position t; the model predicts robustness and collision probability.Source: §II · p. 2

A. SO(3)-Equivariant Scene Encoder

• The SO(3)-equivariant scene encoder represents local object geometry with vector features from one object-centered crop, reusing those features across grasp candidates.Source: A. SO(3)-Equivariant Scene Encoder · p. 3

1) Point Cloud Crop:

• Each crop excludes distant scene geometry while retaining the spatial context needed to evaluate nearby grasp candidates.Source: 1) Point Cloud Crop · p. 3

2) Gated Vector Neurons:

• Gated Vector Neurons use learned smooth multiplicative gates to provide a lightweight nonlinearity while preserving SO(3) equivariance.Source: 2) Gated Vector Neurons · p. 3

3) Equivariant EdgeConv Encoder:

• The encoder applies successive EdgeConv levels with dynamically recomputed k-nearest-neighbor graphs and neighborhood mean pooling.Source: 3) Equivariant EdgeConv Encoder · p. 3
• Equivariant features are retained for candidate alignment while propagated features continue through the encoder; both are candidate-independent and computed once per crop.Source: 3) Equivariant EdgeConv Encoder · p. 3

• Under the row-vector convention, rotating cached features by the grasp orientation yields the same result as rotating the crop into the grasp frame and re-encoding it.Source: 4) Grasp Frame Feature Alignment · p. 3
• The crop origin is expressed in the grasp frame to provide the aligned translation used in subsequent fusion.Source: 4) Grasp Frame Feature Alignment · p. 3

• MAF broadcasts grasp translation across crop points and fuses it point-wise with canonical features at multiple encoder levels before aggregation.Source: B. Mid-level Action Fusion · p. 3
• The fused features combine crop geometry and candidate translation, preserving spatial information across multiple receptive-field scales for grasp robustness and collision predictions.Source: B. Mid-level Action Fusion · pp. 3–4

1) Synthetic Training Data:

• Training uses 500 objects sampled from IPA-3D1K and Thingi10K at a 6:4 ratio, with a disjoint validation set of 100 objects.Source: 1) Synthetic Training Data · p. 4
• The synthetic scenes contain 1–12 settled objects, and each instance receives 100 candidates spanning collision-free antipodal, colliding antipodal, and approach-based grasps.Source: 1) Synthetic Training Data · p. 4
• Approximately 2.5 million training grasps and 0.6 million validation grasps are generated, with roughly 20% positive and 80% negative samples under a robustness threshold of 0.5.Source: 1) Synthetic Training Data · p. 4
• Robustness is the empirical success rate over 25 perturbed physics trials, where success requires lifting an object at least 0.15 m and colliding grasps score zero.Source: 1) Synthetic Training Data · p. 4

2) Training Details:

• Training details specify a five-epoch AdamW schedule, 0.1 m crop radius, 1024-point crops, and joint BCE losses for robustness and collision.Source: 2) Training Details · p. 4
• Fig. 3 shows the simulation evaluation sets: IPA-3D1K, Thingi10K, and scaled Dex-Net adversarial objects.Source: Figure 3 · p. 4

B. Simulation Evaluation Protocol

• Tests use 20 IPA-3D1K objects, 20 challenging Thingi10K objects, and Dex-Net adversarial objects; all are disjoint from training and validation.Dex-Net objects are uniformly scaled by 1.6 to preserve relative object-to-gripper scale.Source: B. Simulation Evaluation Protocol · p. 4
• Evaluation reports grasp success rate in isolated and cluttered settings and declutter rate in cluttered scenes; Dex-Net is tested only in isolation.The IPA-3D1K and Thingi10K cluttered tests use 100 five-object scenes per dataset; isolated objects receive 100 trials each.Source: B. Simulation Evaluation Protocol · p. 4

C. Grasp Planning Pipelines

• Table I compares grasp-evaluation methods across search strategies; reported GSR and DR uncertainties are cluster-bootstrap standard errors.The legend identifies pretrained models and marks best and second-best results within comparison sectors.Source: Table I · p. 5, C. Grasp Planning Pipelines · p. 5
• CEM refinement starts from 256 sampled grasps per object crop, runs 10 iterations with 128 candidates each, and retains the top 25% as elites.The resulting search performs up to 1,536 evaluations per local query; candidates outside the approach-angle constraint or crop radius receive zero quality.Source: C. Grasp Planning Pipelines · p. 5
• The generative-planner strategy scores 1,024 candidate grasps per object from pretrained GraspGen, using simulator ground-truth instance masks to construct simulation inputs.The protocol also measures latency against the number of local queries and latency per query against the number of grasps scored.Source: C. Grasp Planning Pipelines · p. 5, Figure 5 · p. 6

D. Comparison with Baseline Methods in Simulation

• PointNetGPD is the early-fusion baseline, while the retrained GraspGen discriminator is the late-fusion baseline; pretrained EdgeGrasp and OrbitGrasp provide broader pipeline references.The baseline evaluators are trained on the paper’s dataset, whereas the scene-anchored references use publicly available pretrained models.Source: D. Comparison with Baseline Methods in… · p. 6
• At Nq = 5, EquiGQNet reduces CEM planning time from 3.308 s for PointNetGPD to 0.478 s, a 6.9× speedup, while matching early-fusion performance and outperforming late fusion on challenging geometry.The broader scene-anchored comparisons are end-to-end pipeline references, not controlled evaluator comparisons.Source: D. Comparison with Baseline Methods in… · p. 6
• EquiGQNet scales more favorably than PointNetGPD as local-query count Nq grows, and the latency gap increases with the number of grasps Ng scored per query.Planning latency is reported without UOIS segmentation, which averages 54.7 ms; EdgeGrasp and OrbitGrasp remain nearly flat because preprocessing exceeds 90% of per-query latency.Source: D. Comparison with Baseline Methods in… · p. 6
• On cluttered Thingi10K, increasing CEM iterations from 3 to 10 improves GSR/DR by 1.6/3.4 pp for 0.208 s, while increasing GraspGen candidates from 256 to 1024 improves them by 6.1/6.8 pp for 0.175 s.The main experiments use 10 CEM iterations and 1,024 GraspGen candidates.Source: D. Comparison with Baseline Methods in… · p. 6

Effect of Early Scene–Grasp Fusion

• 85.6/89.0% Thingi10K cluttered GSR/DR with translation MAF, versus 63.2/63.8% with global translation fusion, at essentially unchanged planning time.MAF performs comparably to canonicalizing both rotation and translation, without translation-specific scene re-encoding.Source: E. Ablation Study in Simulation · p. 7

Efficient Pose Conditioning with Shared Encoding

• 0.478 s planning time for EquiGQNet and 0.481 s for equivariant feature reuse, versus 7.222 s for candidate-wise canonicalization.Replacing VN-DGCNN with GVN-DGCNN maintains comparable performance and inference cost while increasing training throughput from 5.45 to 7.45 iter/s.Source: E. Ablation Study in Simulation · p. 7
• Explicit rotation alignment with translation MAF is more effective than rotation MAF or global fusion for shared-encoding grasp evaluation.Replacing EquiGQNet’s translation MAF with global fusion causes a large performance degradation; rotation alignment alone improves on fully global fusion but remains relatively weak.Source: E. Ablation Study in Simulation · p. 7

Grasp Quality Prediction Analysis

• EquiGQNet closely matches the strongest candidate-wise canonicalization variants, performs comparably to PointNetGPD, and consistently outperforms the GraspGen discriminator.It retains most of the predictive benefit of candidate-wise canonicalization while reducing planning cost through shared scene encoding.Source: E. Ablation Study in Simulation · p. 7
• Methods conditioning on both grasp rotation and translation before global aggregation produce more localized high-quality regions that better match ground truth, especially on adversarial geometry.Diffuse predictions can create spurious maxima and incorrect grasp selection when objects have narrow graspable regions; pretrained GraspGen predictions also remain diffuse on adversarial geometry.Source: E. Ablation Study in Simulation · p. 7

Effect of Collision Probability in Grasp Scoring

• Using predicted robustness alone instead of robustness multiplied by one minus collision probability changes GSR by at most 0.5 percentage points across simulation settings.The passage attributes the marginal benefit of explicit collision scoring to collision already being reflected in the robustness target.Source: E. Ablation Study in Simulation · p. 7

F. Real-World Experiments

• Ten decluttering runs per method and object set use the same CEM-based continuous refinement, differing only in the grasp evaluator.Each run starts with 12 objects and ends after two consecutive failed attempts; collision-induced emergency stops count as failures.Source: F. Real-World Experiments · p. 7
• EquiGQNet achieves grasp success comparable to PointNetGPD while attaining the highest mean picks per hour on both real-world object sets.The GraspGen discriminator shows a larger performance drop than in simulation, particularly on Dex-Net adversarial objects.Source: F. Real-World Experiments · p. 8

IV. CONCLUSION

• EquiGQNet reuses SO(3)-equivariant scene features while preserving grasp-relative geometry through explicit orientation alignment and pre-aggregation translation fusion.The conclusion reports that this substantially outperforms global late fusion on challenging geometries and yields more localized quality landscapes.Source: §IV · p. 8
• CEM planning remains about 1.9× slower than pure global late fusion, and experiments are limited to tabletop settings with a 45° approach-angle constraint.Evaluation of environments requiring side approaches, such as shelves or bins, remains future work.Source: §IV · p. 8