---
title: Normalized Grasp Space (NGS) Framework
url: https://www.emergentmind.com/topics/normalized-grasp-space-ngs
type: topic
---

# Normalized Grasp Space (NGS) Framework

A Normalized Grasp Space (NGS) is a standardized, size-independent, and alignment-consistent framework for representing and benchmarking the grasping capabilities of robotic hands and grippers. The NGS concept connects functional workspace measurements, kinematic envelope characterizations, and modern deep-learning-based grasp detection, providing a unified metric and geometric substrate for cross-device comparison, learning, and efficient inference in robotic grasp planning. As developed in both optimization-based benchmarking [2106.10402] and region-aware 6-DoF deep grasp detection [2406.01767], NGS underpins data consistency, benchmarking, backbone invariance, and generalization.

## 1. Formal Definition and Rationale

In the context of robotic hands and grippers, NGS provides a mapping from raw kinematic and spatial measurements to a dimensionless unit space, enabling direct quantitative comparison of the grasp workspaces across dissimilar hand designs and gripper scales. For articulated hands, NGS is constructed by specifying a functional grasp coordinate frame “about to grasp” a canonical object (typically a cylinder or sphere), and recording key measurements over representative hand configurations. This space is then normalized along “span” (gripper opening) and “depth” axes to yield a human-interpretable boundary in the unit square $[0,1]^2$ [2106.10402]. 

For deep learning-based 6-DoF grasp detection, NGS is redefined as a local, grasp-centric 3D region around each candidate grasp, aligned and scaled relative to gripper opening width. Each patch is depth-adaptively extracted from sensory data or point clouds and normalized by the reference gripper width, ensuring geometric and scale invariance for all further learning and inference [2406.01767]. This normalization is pivotal for efficient transfer across objects, gripper sizes, and clutter levels.

## 2. Construction of NGS for Robotic Hands

The measurement and normalization protocol for classical hand workspace NGS consists of four steps [2106.10402]:

1. **Functional Grasp Coordinate System**: Define span $(\hat s)$, depth $(\hat d)$, and width $(\hat w)$ axes with reference to the grasp pose on a canonical object. Span runs laterally through the grasp, depth is orthogonal to the palm plane, and width is vertical (table-normal).

2. **Intrinsic Measurements**: Determine hand-specific invariants:
   - $S_{\max}$: Absolute maximum span (fully open).
   - $W_{\min}$: Minimum graspable height (stable two-finger opposition).
   - $W_{\max}$: Maximum achievable height (hand open, resting).

3. **Functional Grasp Workspace Sampling**: For both precision and power grasps, measure span $(s_i)$ and depth $(d_i)$ at three hand configurations: fully open, fully closed, and one intermediate. For spherical grasps, also measure width.

4. **Normalization**: Compute
   \[
   \sigma = \frac{s-s_{\min}}{s_{\max}-s_{\min}}, \quad \delta = \frac{d}{d_{\max}}, \quad (\sigma,\delta)\in[0,1]^2
   \]
   The NGS $N_G$ is the set of such points under the interpolating grasp boundary curve.

Hand workspaces—precision and power—are plotted in $[0,1]^2$, allowing direct area-under-curve style comparison of depth maintenance and envelope across hand types. Example metrics for seven hands are given below:

| Hand                | $s_{\min}$ (mm) | $s_{\max}$ (mm) | $d_{\max}$ (mm) |
|---------------------|-----------------|-----------------|-----------------|
| Model O (Cylindrical) | 10              | 70              | 50              |
| Model O (Spherical)   | 20              | 65              | 55              |
| Barrett (3-finger)    | 15              | 85              | 60              |
| T-42                  | 12              | 80              | 52              |
| Robotiq 2F-85         | 8               | 85              | 58              |
| Kinova Jaco 2 (3f)    | 10              | 75              | 53              |
| Human Right Hand      | 15              | 90              | 65              |

Each $N_G$ curve exposes relative workspace shape, pinch-vs-envelope tradeoff, and possible limitations of specific kinematics.

## 3. NGS in Deep Grasp Detection and Region-Aware Networks

NGS for scene grasp detection is reformulated as a local, normalized, grasp-centric 3D patch:
- For each candidate grasp center $\mathbf{p}_i = (x_i, y_i, z_i)$ and gripper width $w_{\text{gripper}}$, a region of fixed real-world size (typically $2w_{\text{gripper}}$ per side) is resampled from the RGBD observation or point cloud, after accounting for foreshortening and camera intrinsics. This yields a patch $\mathbf{P}_i^{\text{raw}}$.
- XYZ locations are referenced to the patch center and normalized by $w_{\text{gripper}}$ such that all 3D points fall within a $[-1, 1]^3$ cube. Grasp labels $\mathbf{g}_j = (\mathbf{t}_j, \mathbf{R}_j, w_j)$ are mapped into this normalized frame as $\mathbf{g}_j^* = ((\mathbf{t}_j - \mathbf{p}_i)/w_{\text{gripper}}, \mathbf{R}_j, w_j/w_{\text{gripper}})$ [2406.01767].
- The resulting representation, $(x^*,y^*,z^*,\theta,\beta,\gamma,w^*)$, is invariant to translation within the patch, equivariant to in-plane rotation, and scale-invariant.

In RNGNet, these normalized patches feed a coordinate-gated 2D-CNN for 6-DoF grasp prediction. Geometric properties of NGS decouple local grasp feasibility from global scene peculiarities, promoting generalizability and rendering heavy 3D backbones unnecessary.

## 4. Performance Impact and Generalization

NGS has a measurable and significant effect in both benchmarking and deployment scenarios. In benchmarking ($N_G$ curve comparison), hand capability can be visualized and quantified across radically dissimilar designs. For learning-based detection, ablation studies on grasp detection find:

- Without normalization: 66.71/51.66/26.97 AP (Seen/Similar/Novel splits)
- With patch normalization: 69.93/53.15/28.71
- Adding depth-adaptive: 73.98/64.89/30.99
- With full scale randomization: 75.20/66.62/32.38

Furthermore, RNGNet using NGS achieves 58.06 AP (RealSense) on GraspNet and runs at ≈ 50 FPS with only 3.7 M parameters [2406.01767]. Qualitatively, NGS yields denser and more robust grasp proposals, higher physical success rates in cluttered real-world scenes, and direct transfer across objects and gripper sizes.

## 5. Algorithmic Workflow and Loss Functions

In NGS-centric learning pipelines, the forward pass comprises:
- Extraction of depth-adaptive, size-normalized RGBD or point cloud patches centered on candidate grasp points.
- Mapping all points and grasp parameters into the normalized local frame.
- Prediction via a regional multi-grasp generator, attaching discrete rotation anchors and performing classification/regression over locations, angles, and widths.
- Inverse mapping of predicted normalized grasps back to camera or world coordinates.

Supervision is restricted to grasps within a normalized radius ($\|\mathbf{t}^*\| < 0.2$) of the patch center. The loss combines focal components for angle bins and smoothed-L1 terms for residual angles, translations, and width:
\[
L = L_{\theta_{\mathrm{cls}}} + a L_{\theta_{\mathrm{reg}}} + b L_{\gamma\beta} + c L_{t} + d L_{w}
\]

## 6. Relationship to Other Normalized Grasp Representations

NGS is structurally distinct from other normalized or unified grasp representations, such as the Unified Gripper Coordinate Space (UGCS) [2409.14519]. While UGCS maps palm and finger points of a gripper to points on the unit sphere via spherical coordinates to create point-to-point correspondences and transfer grasps across arbitrary grippers, NGS (in both classical and learning-based forms) emphasizes normalization of gripper workspace axes ($\hat{s}$, $\hat{d}$) or grasp-centric patches for local learning and benchmarking. While both frameworks seek gripper-agnostic invariance for improved transfer and comparison, UGCS is optimized for synthesis and exact point-wise transfer, whereas NGS provides both benchmarking envelopes and a practical substrate for local, patch-based learning.

## 7. Assumptions, Limitations, and Scope

Key assumptions underlying NGS include:
- *Functional, not exhaustive*: Only a finite set of poses are sampled for workspace characterization, interpolated with low-order fits. Non-convexities and underactuated workspace regions may be underexplored [2106.10402].
- *Canonical object alignment*: NGS relies on “as-if-grasping” judgments to orient and place the hand with respect to test objects; reproducibility may require supplementary imagery.
- *Contact normal constraints*: Prescribed orientations (e.g., 30° outward for precision, ≥80° for power), but no explicit friction or torque modeling.
- *Shape abstraction*: NGS is best matched to objects approximating canonical primitives (cylinders, spheres); irregular items may require further refinement.
- *Width axis decoupling*: For 2D $N_G$, the width dimension is held constant or omitted except in fully 3D grasp analyses.

In deep learning applications, NGS normalization may be less effective if the real-world patch deviates strongly from geometric assumptions, e.g., when scene clutter or object geometry are extreme. Nonetheless, empirical evaluations indicate robust performance improvements and real-time operation with compact models [2406.01767].

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NGS, in both its workspace-benchmarking and scene-detection manifestations, has become a central tool for the standardized measurement, comparison, and training of robotic grasping across heterogeneous mechanical designs, object populations, and observational regimes [2106.10402, 2406.01767].

Source: https://www.emergentmind.com/topics/normalized-grasp-space-ngs