# Lightweight Convolutional Neural Network with Gaussian-based Grasping
Representation for Robotic Grasping Detection

Hu Cao 1, Guang Chen 1,2∗, Zhijun Li3, Jianjie Lin 1,4, Alois Knoll 1 ∗Guang
Chen is the corresponding author of this workAuthors Affiliation: 1Chair of
Robotics, Artificial Intelligence and Real-time Systems, Technische
Universität München, München , Germany, 2Tongji University, Shanghai, China,
3University of Science and Technology of China, China, 4Fortiss Research
Institute, München , Germany

###### Abstract

The method of deep learning has achieved excellent results in improving the
performance of robotic grasping detection. However, the deep learning methods
used in general object detection are not suitable for robotic grasping
detection. Current modern object detectors are difficult to strike a balance
between high accuracy and fast inference speed. In this paper, we present an
efficient and robust fully convolutional neural network model to perform
robotic grasping pose estimation from n-channel input image of the real
grasping scene. The proposed network is a lightweight generative architecture
for grasping detection in one stage. Specifically, a grasping representation
based on Guassian kernel is introduced to encode training samples, which
embodies the principle of maximum central point grasping confidence.
Meanwhile, to extract multi-scale information and enhance the feature
discriminability, a receptive field block (RFB) is assembled to the bottleneck
of our grasping detection architecture. Besides, pixel attention and channel
attention are combined to automatically learn to focus on fusing context
information of varying shapes and sizes by suppressing the noise feature and
highlighting the grasping object feature. Extensive experiments on two public
grasping datasets, Cornell and Jacquard demonstrate the state-of-the-art
performance of our method in balancing accuracy and inference speed. The
network is an order of magnitude smaller than other excellent algorithms,
while achieving better performance with accuracy of 98.9$\%$ and 95.6$\%$ on
the Cornell and Jacquard datasets, respectively.

###### Index Terms:

Efficient Grasping Detection, Gaussian-based Grasping Representation,
Receptive Field Module, Multi-Dimension Attention Fusion, Fully Convolutional
Neural Network

##  I Introduction

Intelligent robots are widely used in industrial manufacturing fields, such as
human-robot cooperation, robot assembly, and robot welding. The robots need an
effective automated manipulation system to complete the task of picking and
placing. Although grasping is a very simple action for humans, it is still a
challenging task for robots, which involves subsystems such as perception,
planning and extection. Grasping detection is a basic skill for robots to
perform grasping and manipulation tasks in the unstructured enviroments of the
real world. In order to improve the performance of robotic grasping, it is
necessary to develop a robust algorithm to predict the location and
orientation of the grasping objects.

Early grasping detection works are mainly based on traditional methods, such
as serach algorithm. However, these algorithms cannot work effectively in
complex real scenarios [1]. In recent years, deep learning-based methods have
achieved excellent results in robotic grasping detection. Based on two-
dimension space can be projected into the three-dimensional space to guide the
robot to grasp, a five-dimensional grasp configuration is proposed to
represent grasp rectangle [2]. Due to the simplification of the grasping
object dimension, the deep convolutional neural network can be used to learn
extracting features mroe suitable for specific tasks than hand-engineered
features by taking 2-D images as input. Many works, such as [3, 4, 5, 6],
train the neural network to predict the grasping rectangle of objects, and
select the one with the highest grasp probability score from multiple grasp
candidate rectangles as the best grasp result. Some one or two-stage deep
learning methods [7, 8, 9] that have achieved great success in object
detection have been modified to perform grasping detection task. For example,
[10] refers to some key ideas of Faster RCNN [9] in the field of object
detection to carry out robotic grasping from the input RGB-D images. In
addition, other works, such as [5, 11], implemented high-precision grasp
detection on Cornell grasping dataset based on the one stage object detection
method [7, 8]. Although these object detection-based methods achieve better
accuracy in robotic grasping detection, their design based on horizontal
rectangular box is not suitable for angular grasp detection task, and most of
them have complex network structure, so it is difficult to achieve a good
balance in detection accuracy and speed. In [12, 13], the authors improve the
performance of grasping detection by demploying an oriented anchor box
mechanism to match the grasp rectangles. However, although these methods have
achieved some improvement in accuracy or speed, the size of network parameters
of their algorithms is still too large to be suitable for real-time
applications. To solve these problems mentioned above, a new grasping
representation is proposed by [14]. Different from previous works, which used
the method of sampling grasping candidate rectangle, [14] applies generated
convolutional neural network to directly regress grasp points, which
simplifies the definition of grasping representation and achieves high real-
time performance based on the lightweight architecture. Inspired by [14], the
authors of [15, 16] utilize some ideas of algorithms in vision segmentation
tasks to predict robotic grasping pose from extracted pixel-wise features.
Recently, the residual structure is introduced into the generated neural
network model [17], which achieved state-of-the-art grasping detection
accuracy on Cornell and Jacquard grasping datasets. However, they all have a
shortcoming that although they take the location with the largest grasping
score as the center point coordinate, they fail to highlight the importance of
the largest grasping probability at the center point.

In this work, we utilize 2-D Guassian kernel to encode training samples to
emphasize that the center point position with the highest grasping confidence
score. On the basis of Guassian-based grasping representation, we develop a
lightweight generative architecture for robotic grasping pose estimation.
Referring to the receptive field structure in human visual system, we combine
the residual block and a receptive field block module in the bottleneck layer
to enhance the feature discriminability and robustness. In addition, in order
to reduce the information loss in the sampling process, we fuse low-level
features with depth features in the decoder process, and use a multi-
dimensional attention network composed of pixel attention network and channel
attention network to suppress redundant features and highlight meaningful
features in the fusion process. Extensive experiments demonstrate that our
algorithm achieves state-of-the-art performance in accuracy and inference
speed on the public grasping datasets Cornell and Jacquard with a small
network parameter size. Concretely, the main contributions of this paper are
as follows:

  * •

We propose a Gaussian-based grasping representation, which relects the maximum
grasping score at the center point location and can signigicantly improve the
grasping detection accuracy.

  * •

We develope a lightweight generative architecture which achieves high
detection accuracy and real-time running speed with small network parameters.

  * •

A receptive field block module is embedded in the bottleneck of the network to
enhance its feature discriminability and robustness, and a multi-dimensional
attention fusion network is developed to suppress redundant features and
enhance target features in the fusion process.

  * •

Evaluation on the public Cornell and Jacquard grasping datasets demonstrate
that the proposed generative based grasping detection algorithm achieves
state-of-the-art performance of both speed and detection accuracy.

The rest of this paper is organized as follows: previous works related to the
grasp detection are reviewed in section 2. Robotic grasping system is
introduced in section 3,. Detailed description of the proposed grasping
detection method is illustrated in section 4. Dataset analysis is presented in
section 5. Experiments based on the public grasping datasets, Cornell and
Jacquard are discussed in section 6. Finaly, we conclude our work in section
7.

##  II Related Work

For 2D planar robotic grasping where the grasp is constrained in one
direction, the methods can be divided into oriented rectangle-based grasp
representation methods and contact point-based grasp representation methods.
The comparision of the two grasp representations are presented in Fig. 1. We
will review the relevant works below.

Figure 1: A comparision between the methods of oriented rectangle-based grasp
representation and the methods of contact point-based grasp representation.
The top branch is the workflow of the model using the oriented rectangle as
grasp representation, and the bottom branch is the workflow of the model using
the contact point grasp representation.

###  II-A Methods of oriented rectangle-based grasp representation

The goal of grasping detection is to find the appropriate grasp pose for the
robot through the visual information of the grasping object, so as to provide
reliable perception information for subsequent planning and control process,
and achieve successful grasp. Grasp is a widely studied topic in the field of
robotics, and the approaches used can be summmarized as anlytic methods and
empirical methods. The analytical methods use mathematical and physical models
in geometry, motion and dynamics to carry out the calculation for grasping
[18]. Its theoretical foundation is solid, but the deficiency lies in that the
model between the robot manipulator and the grasping object in the real
3-dimensional world is very complex, and it is difficult to realize the model
with high precision. In contrast, empirical methods do not strictly rely on
real-world modeling methods, and some works utilize data information from
known objects to build models to predict the grasping pose of new objects [19,
20, 21]. A new grasp representation is proposed in [22], where a simplified
five-dimensional oriented rectangle grasp representation is used to replace
the seven-dimensional grasp pose consisting of 3D location, 3D orientation and
the opening and closing distance of the plate gripper. Based on the oriented
rectangles grasp configuration, the deep learning approaches can be
successfully applied to the grasping detection task, which mainly include
classification-based methods, regression-based methods and detection-based
methods [23].

Classification-based Methods: A first deep learning-based robotic grasing
detection method is presented in [2], the authors achieve excellent results by
using a two-step cascaded structure with two deep networks. In [24], grasping
proposals are estimated by sampling grasping locations and adjacent image
patches. The grasp orientation is predicted by dividing angle into 18
disccrete angles. Since grasping dataset is scant, a large simulation database
called Dex-Net 2.0 is built in [25]. On the basis of Dex-Net 2.0, a Grasp-
Quality Covolutional Neural Network (GQ-CNN) is developed to classify the
potential grasps. Although the network is trained on synthetic data, the
proposed method still works well in the real world. Moreover, a
classification-based robotic grasping detection method with spatial
transformer network (STN) is proposed in [26]. The results of evalating on
Cornell grasping dataset indicate that their multi-stage STN algorithm peforms
well. The grasping detection method based on classification is a more direct
and reasonable method, many aspects of which are worth further study.

Regression-based Methods:  Regression-based methods is to directly predict
grasp parameters of location and orientation by training a model. A first
regression-based single shot grasping detection approach is proposed in [3],
in which the authors use AlexNet to extract feature and achieve real-time
performance by removing the process of searching potential grasps. Combing RGB
and depth data, a multi-modal fusion method is introduced in [27]. With fusing
RGB and depth features, the proposed method directly regress the grasp
parameters and improve the grasping detection accuracy on the Cornell grasping
dataset. Similar to [27], the authors of [28] use ResNet as backbone to
integrate RGB and depth information and further improves the performance of
grasping detection. In addition, a graping detection method based on ROI
(Region of Interest) is proposed in [21]. In this work, the authors regress
grasp pose on ROI features and achieve better performance in object
overlapping challenge scene. The regression-based method is effective, but its
disadvantage is that it is more incilined to learn the mean value of the
ground truth grasps.

Detection-based Methods:  Many detection-based methods refer to some key ideas
from object detection, such as anchor box. Based on the prior knowledge of
these anchor boxes, the regression problem of grasping parameters is
simplified. In [29], vision and tactile sensing are fused to build a hybrid
architecture for robotic grasping. The authors use anchor box to do axis
aligned and grasp orientation is predicted by considering grasp angle
estimation as classification problem. The grasp angle estimation methods used
in [29] is extened by [10]. By transforming the angel estimation into
classification problem, the method of [10] achieves high grasping detection
accuracy on Cornell dataset based on FasterRCNN [9]. Different from the
horizontal anchor box used in object detection, the authors of [12] specially
design an oriented anchor box mechanism for grasping task and improve the
performance of model by combing end-to-end fully convolutional neural network.
Morever, [30] further extend the method of [12] and proposes a deep neural
network architecture that performs better on the Jacquard dataset.

###  II-B Methods of contact point-based grasp representation

The grasping representation based on oriented rectangle is widely used in
robotic grasping detection task. In terms of the real plate grasping task, the
gripper does not need so much information to perform the grasping action. A
new simplified contact point-based grasping representation is introduced in
[14], which consists of grasp quality, center point, oriented angle and grasp
width. Based on this grasping representation, GGCNN and GGCNN2 are developed
to predict the grasping pose, and their methods achieve excellent performance
in both detection accuracy and inference speed. Refer to [14], the grasping
detection performance is improved by a fully convolutional neural network with
pixel-wise way in [15]. Both [14] and [15] take depth data as input, a
generative residual convolutional neural network is proposed in [17] to
generate grasps, which take n-channel images as input. Recently, the authors
of [16] take some ideas from image segmentation to perform three-finger
robotic grasping detection. Similar to [16], a orientation attentive grasp
synthesis (ORANGE) framwork is developed in [31], which achieves better
results on Jacquard dataset based on the GGCNN and Unet model. In this paper,
we propose a Guassian-based grasping representation to highlight the
importance of center point. We further develop a lightweight generative
architecture for robotic grasping detection, which performs well in inference
speed and accuracy on two public datasets, Cornell and Jacquard.

##  III Robotic Grasping System

In this section, we give an overview of the robotic grasping system settings
and illustrate the principles of Gaussian-based grasping representation.

###  III-A System Setting

A robotic grasping system usually consists of a robot arm, perception sensors,
grasping objects and workspace. In order to complete the grasping task
successfully, not only the grasp pose of objects needs to be obtained, but the
subsystem of planning and control is involved. In grasping detection part, we
consider limiting the manipulator to the normal direction of the workspace so
that it becomes a goal for perception in 2D space. Through this setting, most
of the grasping objects can be considered as flat objects by placing them
reasonably on the workbench. Instead of building 3D point cloud data, the
whole grasping system can reduce the cost of storage and calculation and
improve its operation capacity. The grasp pose of flat objects can be treated
as a rectangle. Since the size of each plate gripper is fixed, we use a
simplified grasping representation mentioned in section II-B to perform grasp
pose estimation.

###  III-B Gaussian-based grasp representation

For given RGB images or depth information of different objects, the grasping
detection system should learn how to obtain the optimal grasp configuration
for subsequent tasks. Many works, such as [29, 10, 12], are based on five-
dimensional grasping representation to generate grasp pose.

$g=\left\\{x,y,\theta,w,h\right\\}$ (1)

where, $(x,y)$ is the coordinates of the center point, $\theta$ represents the
orientation of the grasping rectangle, and the weight and height of the
grasping rectangle are denoted by $(w,h)$. Rectangular box is frequently used
in object detection, but it is not suitable for grasping detection task. As
the size of gripper is usually a known variable, a simplified representation
is introduced in [14] for high-precision, real-time robotic grasping. The new
grasping representation for 3-D pose is defined as:

$g=\left\\{\textbf{p},\varphi,w,q\right\\}$ (2)

where, the center point location in Cartesian coordinates is
$\textbf{p}=(x,y,z)$. $\varphi$ and $w$ are the rotation angle of the gripper
around the $z$ axis and the opening and closing distance of the gripper,
respectively. Sicne the five-dimensional grasping representation lacks the
scale factor to evaluate the grasping quality, $q$ is added to the new
representation as a scale to measure the probability of grasp success. In
addition, the definition of the new grasping representation in 2-D space can
be described as,

$\hat{g}=\left\\{\hat{p},\hat{\varphi},\hat{w},\hat{q}\right\\}$ (3)

where, $\hat{p}=(u,v)$ represents the center point in the image coordinates.
$\hat{\varphi}$ denotes the orientation in the camera frame. $\hat{w}$ and
$\hat{q}$ still represent the opening and closing distance of the gripper and
the grasp quality, respectively. When we know the calibration result of the
grasping system, the grasp pose $\hat{g}$ can be converted to the world
coordinates $g$ by matrix operation,

$g=T_{RC}(T_{CI}(\hat{g}))$ (4)

where, $T_{RC}$ and $T_{CI}$ represent the transform matrices of the camera
frame to the world frame and 2-D image space to the camera frame respectively.
Moreover, the grasp map in the image space is denoted as:

$\textbf{G}=\left\\{\Phi,W,Q\right\\}\in{\mathbb{R}^{3\times W\times H}}$ (5)

where, each pixel in the grasp maps, $\Phi,W,Q$, is filled with the
corresponding $\hat{\varphi},\hat{w},\hat{q}$ values. In this way, it can be
ensured that the center point coordinates in the subsequent inference process
can be found by searching for the pixel value of the maximum grasp quality,
$\hat{g^{*}}=max_{\hat{Q}}\hat{G}$. In [14], the authors filled a rectangular
area around the center point with 1 indicating the highest grasping quality,
and the other pixels were 0. The model is trained by this method to learn the
maximum grasp quality of the center point. Because all pixels in the
rectangular area have the best grasping quality, it leads to a defect that the
importance of the center point is not highlighted, resulting the ambiguity to
the model. In this work, we use 2-D Gaussian kernel to regularize the grasping
representation to indicate where the object center might exist, as is shown in
Fig. 2. The novel Gaussian-based grasping representation is represented as
$g_{k}$, the corresponding Gaussian-based grasp map is defined as:

$\displaystyle G_{K}$
$\displaystyle=\left\\{\Phi,W,Q_{K}\right\\}\in{\mathbb{R}^{3\times W\times
H}}$ (6) $\displaystyle where,$ $\displaystyle Q_{K}$
$\displaystyle=K(x,y)=exp(-\frac{(x-x_{0})^{2}}{2\sigma_{x}^{2}}-\frac{(y-y_{0})^{2}}{2\sigma_{y}^{2}})$
$\displaystyle where,$ $\displaystyle\sigma_{x}$
$\displaystyle=T_{x},\sigma_{y}=T_{y}$

In Eq. 6, the generated grasp quality map is decided by the center point
location $(x_{0},y_{0})$, the parameter $\sigma_{x}$ and $\sigma_{y}$, and the
corresponding scale factor $T_{x}$ and $T_{y}$. By this method, the peak of
Gaussian distribution is the center coordinate of the grasp rectangle. In this
work, we will discuss the impact of parameter settings in more detail in
section VI-F.

Figure 2: Gaussian-based grasp representation: The 2-D Gaussian kernel is
applied to the grasp quality map to highlight the max grasp quality of its
central point position. (a) the schematic diagram of grasp quality weight
distribution after 2-D Gaussian function deployment, and (b) the schematic
diagram of grasp representation. Figure 3: The structure of our lightweight
generative grasping detection algorithm. I and Conv denote the input data and
covolution filter, respectively. The proposed method consisits of the
downsampling block, the bottleneck layer, the multi-dimensional attention
fusion network and the upsampling block.

##  IV Method

In this section, we introduce a lightweight generative architecture for
robotic grasping detection. Fig. 3 presents the structure of our grasping
detection model. The input data is transformed by downsampling block into
feature maps with smaller size, more channels and richer semantic information.
In the bottleneck, resnet block and multi-scale receptive fields block module
are combined to extract more discriminability and robustness features.
Meanwhile, a multi-dimensional attention fusion network consisted of pixel
attention sub-network and channel attention sub-network is used to fuse
shallow and deep semantic features before upsampling, while suppressing
redundant features and enhancing the meaningful features during the fusion
process. Finally, based on the extracted features, four task-specific sub-
networks are added to predict grasp quality, angle (the form of $sin(2\theta)$
and $cos(2\theta)$), and width (the opening and closing distance of the
gripper) respectively. We will illustrate the details of each component of the
proposed grasping network.

###  IV-A Basic Network Architecture

The proposed generative grasping architecture is composed of the downsampling
block, the bottleneck layer, the multi-dimensional attention fusion network
and the upsampling block, as shown in Fig. 3. A downsampling block consists of
covolution layer with kernel size of 3x3 and maximum pooling layer with kernel
size of 2x2, which can be represented as Eq. 7.

$x_{d}=f_{maxpool}(f_{conv}^{n}(f_{conv}^{n-1}(...f_{conv}^{0}(I)...)))$ (7)

In this work, we use 2 down-sampling blocks and 2 convolutional layers in the
down-sampling process. Specifically, the first down-sampling block is composed
of 4 convolutional layers (n = 3) and 1 maximum pooling layer, and the second
down-sampling layer is composed of 2 convolutional layers (n = 1) and 1
maximum pooling layer. After the down-sampled data pass through 2
convolutional layers, they are fed into a bottleneck layer consisting of 3
residual blocks (k = 2) and 1 receptive fields block module (RFBM) to further
extract features. Since RFBM is composed of vary scale convolutional filters,
we can acquire more rich image details. More details about RFBM will be
discussed in section IV-B. The output of the bottleneck can be formulated as
Eq. 8.

$x_{b}=f_{RFBM}(f_{res}^{k}(f_{res}^{k-1}(...f_{res}^{0}(f_{conv}^{1}(f_{conv}^{0}(x_{d})))...)))$
(8)

The output $x_{b}$ of the bottleneck is fed into multi-dimensional attention
fusion network (MDAFN) and up-sampling block. The multi-dimensional attention
fusion network composed of pixel attention and channel attention subnetwork
can suppress the noise feature and enhance the effective feature during the
fusion of shallow feature and deep feature. The MDAFN will be illustrated in
more detail in section IV-C. In upsampling block, the pixshuffle layer [32] is
used to increase feature resolution with the scale factor set to 2. In this
work, the number of multi-dimensional attention fusion networks and upsampling
blocks are both 2, and the output can be expressed as Eq. 9.

$x_{u}=f_{pixshuffle}^{1}(f_{MDAFN}^{1}(f_{pixshuffle}^{0}(f_{MDAFN}^{0}(x_{b}))))$
(9)

Final network layer is composed of 4 task-specific convolutional filters with
kernel size 3x3. The final output results can be given as Eq. 10.

$\displaystyle g_{q}$ $\displaystyle=max_{q}(f_{conv}^{0}(x_{u})),$ (10)
$\displaystyle g_{cos(2\theta)}$ $\displaystyle=max_{q}(f_{conv}^{1}(x_{u})),$
$\displaystyle g_{sin(2\theta)}$ $\displaystyle=max_{q}(f_{conv}^{2}(x_{u})),$
$\displaystyle g_{w}$ $\displaystyle=max_{q}(f_{conv}^{3}(x_{u})),$

where, the position of the center point is the pixel coordinates of the
largest grasp quality $g_{q}$, the opening and closing distance of the gripper
is $g_{w}$, and the grasp angle can be computed by
$g_{angle}=arctan(\frac{g_{sin(2\theta)}}{g_{cos(2\theta)}})/2$.

Figure 4: Receptive field block module.

###  IV-B Multi-scale Receptive Fields Block Module

In neuroscience, researchers have found that there is a eccentricity function
in the human visual cortex that adjusts the size of the receptive field of
vision [33]. This mechanism can help to emphasize the importance of the area
near the center. In this work, we introduce a multi-scale receptive field
block (RFB) [34] to assemble the bottleneck layer of our grasping detection
architecture for improving the ability of extracting multi-scale information
and enhancing the feature dicriminability. The receptive field block module is
composed of multi-branch covolution layers with different kernels
corresponding to the receptive fields of different sizes. Moreover, the
dilated convolution layer is used to control the eccentricity, and the
features extracted by the branches of the different receptive fields are
recombined to form the final representation, as shown in Fig 4. In each
branch, the convolutional layer with a specific kernel size is followed by a
dilated convolutional layer with a corresponding dilation rate, which uses a
combination of different kernel sizes (1x1, 3x3, 7x1, 1x7). The features
extracted from the four branches are concatenated and then added to the input
data to obtain the final multi-scale feature output.

Figure 5: Multi-dimensional attention fusion network. The top branch is the
pixel-level attention subnetwork, and the bottom branch is the channel-level
attention subnetwork.

###  IV-C Multi-dimensional Attention Fusion Network

When humans look at an image, we don’t pay attention to everything in the
image, but instead focus on what’s interesting to us. The attention mechanism
in the visual system focuses limited attention on the important information,
thus saving resources and obtaining the most effective information quickly. In
the field of computer vision, some attention mechanisms with few parameters,
fast speed and excellent effect have been developed [35, 36, 37, 38]. In order
to perceive the grasping objects effectively from the complex background, a
multi-dimensional attention network composed of pixel attention subnetwork and
channel attention subnetwork is designed to suppress the noise feature and
highlight the object feature, as shown in Fig. 5. Specificaly, the shallow
features and the deep features are concatenated together, and the fused
features are fed into a multi-dimensional attention network to automatically
learn the importance of the fused features at the pixel level and the channel
level. In pixel attention subnetwork, the feature map F passes through a 3x3
covolution layer to generate an attention map by covolution operation. The
attention map is further computed with sigmoid to abtain the corresponding
pixel-wise weight score. Moreover, SENet [36] is used as the channel attention
subnetwork, which obtains 1x1xC features through global average pooling, and
then uses two fully connection layers and the corresponding activation
function Relu to build the correlation between channels, and finally outputs
the weight score of the feature channel through sigmoid operation. Both the
pixel-wise and channel-wise weight maps are multiplied with the feature map F
to obtain a novel output with reduced noise and enhanced object information.

###  IV-D Loss Function

For a dataset including grasping objects $O=\left\\{O_{1}...O_{n}\right\\}$,
input images $I=\left\\{I_{1}...I_{n}\right\\}$, and corresponding grasp
labels $L=\left\\{L_{1}...L_{n}\right\\}$, We propose a lightweight fully
convoluton neural network to approximate the complex function
$F:I\longmapsto\hat{G}$, where $F$ represents a neural network model with
weighted parameters, $I$ is input image data, and $\hat{G}$ denotes grasp
prediction. We train our model to learn the mapping function F by optimizing
the minimum error between grasp prediction $\hat{G}$ and the corresponding
label $L$. In this work, we consider the grasp pose estimation as regression
problem, therefore the Smooth L1 loss is used as our regression loss function.
The loss function $L_{r}$ of our grasping detection model is defined as :

$\displaystyle
L_{r}(\hat{G},L)=\sum_{i}^{N}\sum_{m\in{\\{q,cos2\theta,sin2\theta,w\\}}}Smooth_{L1}(\hat{G}_{i}^{m}-L_{i}^{m})$
(11)

where $Smooth_{L1}$ is formulated as:

$Smooth_{L1}(x)=\begin{dcases}(\sigma x)^{2}/2,&\text{if}\>|x|\textless 1;\\\
|x|-0.5/\sigma^{2},&\text{otherwise}.\end{dcases}$

where $N$ is the number of grasp candidates. $q,w$ represent the grasp quality
and the opening and closing distance of the gripper, respectively, and
$(cos(2\theta),sin(2\theta))$ is the form of orientation angle. In
$Smooth_{L1}$ fuction, $\sigma$ is the hyperparameter that controls the smooth
area, and it is set to 1 in this work.

Figure 6: Qualitative images from Cornell grasping dataset. Figure 7:
Qualitative images from Jacquard grasping dataset.

##  V Dataset Analysis

Since the deep learning has become popular, large public datasets, such as
ImageNet, COCO, KITTI, etc, have been driving the progress of algorithms.
However, in the field of robotic grasping detection, the number of available
grasping datasets is insufficient. Dexnet, Cornell, and Jacquard are famous
common grasping datasets that serve as a platform to compare the performance
of the state-of-the-art grasping detection algorithms. In Tab. I, it presents
a summary of the different grasping datasets.

Dexnet Grasping Dataset:  The Dexterity Network (Dex-Net) is a research
project established by UC Berkeley Automation Lab that provides code, dataset,
and algorithms for grasping task. At present, the project has released four
versions of the dataset, namely Dex-Net 1.0, Dex-Net 2.0, Dex-Net 3.0, and
Dex-Net 4.0. Dex-Net 1.0 is a synthetic dataset with over 10000 unique 3D
object models and 2.5 million corresponding grasp labels. Based on Dex-Net
1.0, thousands of 3D objects with arbitrary poses are used to generate more
than 6.7 million ponit clouds and grasps, which constitute the Dex-Net 2.0
dataset. Dex-Net 3.0 is built to study the grasp using suction-based end
effectors. Recently, a extension of previous versions, Dex-Net 4.0, has been
developed, which can perform training for parallel-jaw and suction gripper.
Since Dex-Net dataset includes only synthetic point cloud data and no RGB
information of the grasp objects, the experiment of this work is mainly
carried out on Cornell and Jacquard grasping dataset.

Cornell Grasping Dataset:  The Cornell dataset, which is widely used as a
benchmark evaluation platform, was collected in the real world with the RGB-D
camera. Some example imgaes are shown in Fig 6. The dataset is composed of 885
images with a resolution of 640$\times$480 pixels of 240 different objects
with positive grasps (5110) and negative grasps (2909). RGB images and
corresponding point cloud data of each object with various poses are provided.
However, the scale of Cornell dataset is small for training our convolutional
neural network model. In this work, we use online data augement methods
including random cropping, zooms and rotation to extend the dataset to avoid
overfitting during training.

Jacquard Grasping Dataset:  Jacquard is a large grasping dataset created
through simulation based on CAD models. Because no manual collection and
annotation is required, the Jacquard dataset is larger than the Cornell
dataset, containing 50k images of 11k objects and over 1 million grasp labels.
In Fig. 7, it presents some images from the Jacquard datset. Furthermore, the
dataset also provides a standard simulation environment to perform simulated
grasp trials (SGTs) under a consistent condition for different algorithms. In
this work, we use SGTs as a benchmark to fairly compare the performance of
various algorithms in the robot arm grasp. Since the Jacquard dataset is large
enough, we do not use any data auguement methods to it.

TABLE I: Description of the public Grasping Datasets Dataset |  Modality |  Objects |  Images |  Grasps
---|---|---|---|---
Dexnet |  Depth |  1500 |  6.7M |  6.7M
Cornell |  RGB-D |  240 |  885 |  8019
Jacquard |  RGB-D |  11K |  54K |  1.1M

##  VI Experiment

To verify the generalization capability of the proposed lightweight generative
model, we conducted experiments on two public grasping datasets, Cornell and
Jacquard. Extensive experiments results indicate that our algorithm has high
inference speed while achieving high grasp detection accuracy, and the size of
network parameters is an order of magnitude smaller than most previous
excellent algorithms. In addition, we also explore the impact of different
network designs on algorithm performance and discuss the shortcomings of our
method.

TABLE II: Detection Accuracy (%) of Different Methods on Cornell Dataset Author | Method | Input Size | Accuracy(%) | Time (ms)
---|---|---|---|---
Image-Wise | Object-Wise
Jiang [22] | Fast Search | 227 $\times$ 227 | 60.5 | 58.3 | 5000
Lenz [2] | SAE | 227 $\times$ 227 | 73.9 | 75.6 | 1350
Karaoguz [39] | GRPN | - | 88.7 | - | 200
Chu [10] | FasterRcnn | 227 $\times$ 227 | 96.0 | 96.1 | 120
Zhang [27] | Multimodal Fusion | 224 $\times$ 224 | 88.9 | 88.2 | 117
Zhou [12] | FCGN | 320 $\times$ 320 | 97.7 | 96.6 | 117
Wang [40] | Two-stage, Cloosed Loop | - | 85.3 | - | 140
Redmon [3] | AlexNet, MultiGrasp | 224 $\times$ 224 | 88.0 | 87.1 | 76
Kumra [28] | ResNet-50 | 224 $\times$ 224 | 89.2 | 88.9 | 103
Kumra [17] | GR-ConvNet | 300$\times$ 300 | 97.7 | 96.8 | -
Asif [41] | GraspNet | 224 $\times$ 224 | 90.6 | 90.2 | 24
Guo [29] | ZF-Net, MultiGrasp | - | 93.2 | 89.1 | -
Park [11] | FCNN | 360$\times$ 360 | 96.6 | 95.4 | 20
Morrison [14] | GGCNN | 300$\times$ 300 | 73.0 | 69.0 | 3
Zhang [21] | ROI-GD | - | 93.6 | 93.5 | 40
Song [14] | Matching Strategy | 320$\times$ 320 | 96.2 | 95.6 | -
Wang [42] | GPWRG | 400$\times$ 400 | 94.4 | 91.0 | 8
Our | Efficient Grasping-D | 300$\times$ 300 | 98.9 | 95.5 | 6
Efficient Grasping-RGB | 96.6 | 91.0 | 6
Efficient Grasping-RGB-D | 98.9 | 97.8 | 6
Figure 8: The detection results of grasping network on Cornell dataset. The
first three rows are the maps for grasp quality, angle and width representing
the opening and closing distance of the gripper. And, the last row is the best
grasp outputs for several objects. Figure 9: The detection results of grasping
network on Jacquard dataset. The first three rows are the maps for grasp
quality, angle and width representing the opening and closing distance of the
gripper. And, the last row is the best grasp outputs for several objects.

###  VI-A Evaluation Metrics

Simillar to many previous works, the metric used in this paper to evaluate our
model on the Cornell and Jacquard datasets is rectangle metric. Specifically,
a pridicted grasp is regarded a correct grasp when it meets the following two
conditions:

  * •

Angle difference: the difference of orientation angle between the predicted
grasp and corresponding grasp label is less than $30^{\circ}$ .

  * •

Jaccard index: the Jaccard index of the predicted grasp and corresponding
grasp label is greater than 25%, which can be formulated as Eq. 12.

$J(g_{p},g_{l})=\frac{|g_{p}\cap g_{l}|}{g_{p}\cup g_{l}}$ (12)

where $g_{p}$ and $g_{l}$ denote the predicted grasp rectangle and the area of
the corresponding grasp label, respectively. $g_{p}\cap g_{t}$ represents the
intersection of predicted grasp and the corresponding grasp label. And the
union of predicted grasp and the corresponding grasp label is represented as
$g_{p}\cup g_{t}$.

###  VI-B Data preprocessing

The experiments for this work are performed on the Cornell and Jacquard
grasping dataset. Due to the small data size of Cornell, we conducted online
data augmentation to train our network. Meanwhile, Jacquard dataset has
sufficient data, so we train the network directly on it without adopting any
data augmentation method. The images of Cornell and Jacquard are resized to
300x300 to feed into the network. In addition, the data labels are encoded for
training. A 2D Gaussian kernel is used to encode each ground-truth positive
grasp so that the corresponding region satisfies the Gaussian distribution,
where the peak of the Gaussian distribution is the coordinate of the center
point. We also use $sin(2\theta)$ and $cos(2\theta)$ to encode the grap angle,
where $\theta\in[-\frac{\pi}{2},\frac{\pi}{2}]$. The resulting corresponding
valuses range from -1 to 1. By using this method, ambiguity can be avoided in
the Angle learning process, which is beneficial to the convergence of the
network. Similarly, the grasp width representing the opening and closing
distance of the gripper is scaled to a range of 0 to 1 during the training.

###  VI-C Training Methodology

In training period, we train our generative model end to end on a Nvidia
GTX2080Ti GPU with 22GB memory. The grasping network is achieved based on
Pytorch 1.2.0 with cudnn-7.5 and cuda-10.0 pacakges. The popular Adam
optimizer is used to optimize the network for back propagation during training
process. Futhermore, The initial learning rate is defiend as 0.001 and the
batch size of 8 is used in this work.

###  VI-D Experiments on Cornell Grasping Dataset

Following the previous works [10, 12, 13], the Cornell dataset is divided into
two different ways to validate the generalization ability of the model:

  * •

Image-wise level: the images of dataset are randomly divided. The images of
each grasp object in the training set and test set are different. Image-wise
level method is used to test the generalization ability of the network to new
grasp pose.

  * •

Object-wise level: the object instances of dataset are randomly divided. All
the images of the same object are split into the same set (training set or
test set). Object-wise level method is used to validate the generalization
ability of the network for new object, which is not seen in the training
process.

The comparison of the grasp detection accuracy of our model and other methods
on the Cornell dataset is presented in Table. II. Experiment results indicate
that the proposed grasp detection algorithm achieves high accuracy of 98.9$\%$
and 97.8$\%$ in image-wise and object-wise split with an inference time of
6ms. Compared with other state-of-the-art algorithms, our model maintains a
better balance betweeen accuracy and real-time performance. By changing the
mode of input data, we can find that our generated grasping detection
achitecture can get excellent performance with the input of depth data. And,
the results in object-wise split demonstrate that the combination of depth
data and RGB data with rich color and texture information enables the model to
have more robust generalization ability to unseen objects. In Fig. 8, we plot
the grasping detection results of some objects for display. Only the grasp
candidate with the highest grasp quality is selected as the final output, and
the top-1 grasp is visualised in the last row. The first three rows are the
maps for grasp quality, angle and width representing the opening and closing
distance of the gripper. It can be seen from the figure that our algorithm can
provide reliable grasp candidate for objects with different shapes and poses.

TABLE III: Detection Accuracy (%) of Different Methods on Jacquard Dataset Author |  Method |  Accuracy($\%$)
---|---|---
Depierre [43] |  Jacquard |  74.2
Morrison [14] |  GG-CNN2 |  84
Zhou [12] |  FCGN-RGD |  92.8
Zhang [21] |  ROIGD-RGD |  93.6
Song [13] |  Resnet-101-RGD |  93.2
Kumra [17] |  GR-ConvNet-RGB-D |  94.6
Ours |  Efficient Grasping-D |  95.6
Efficient Grasping-RGB |  91.6
Efficient Grasping-RGB-D |  93.6

###  VI-E Experiments on Jacquard Grasping Dataset

Similar to the Cornell dataset, we trian our network on Jacquard dataset to
perform grasp pose estimation. The results are summarized in Table. III.
Taking depth data as input, the proposed method obtains state-of-the-art
performance with a detection accuracy of 95.6$\%$, which exceeds the existing
methods and reaches the best result on Jacquard dataset. The experimental
results in Table. II and Table. III demonstrate that our algorithm not only
achieves excellent performance on the Cornell dataset but also outperforms
other methods on the Jacquard dataset. Some detection examples are displayed
in Fig. 9. As with the Cornell dataset, grasp quality, Angle, width
representing the opening and closing distance of the gripper, and the best
detection results on the jacquard dataset are presented in the figure.

TABLE IV: The impact of different network Settings on detection performance \+ GGR |  |  ✓ |  ✓ |  ✓
---|---|---|---|---
\+ RFBM |  ✓ |  |  ✓ |  ✓
\+ MDAFN |  ✓ |  ✓ |  |  ✓
Acurracy ($\%$) |  97.8 |  94.4 |  96.6 |  98.9
Figure 10: The grasp detection accuracy when using different scale factors of
Gaussian kernel

###  VI-F Ablation Study

In order to further explore the impact of different components on grasping
pose learning, we trained our models of different network Settings in image-
wise split of Cornell dataset with RGBD data as input. The experimental
results are summarized in Table. IV. It can be obtained from the detection
accuracy evaluation results in the Table. IV that Gaussian-based grasp
representation (GGR), receptive field block module (RFBM) and multi-
dimensional attention fusion network (MDAFN) can all bring performance
improvement to the network, and all components combined together can get the
best grasping detection performance. Moreover, we also discuss the impact of
different scale factor Settings (T) on the model, as shown in the Fig. 10. In
this work, the scale factors $T_{x}$ and $T_{y}$ mentioned in section III-B
are set to $Tx=Ty=T$ with values ranging from $\left\\{4,8,16,32,64\right\\}$.
When the $T=16$ , the model in object-wise split of Cornell dataset reaches
the best detection accuracy of 97.8. In the process of experiment, we found
the different density of annotation for a particular dataset should be set the
size of the corresponding scale factor value, which can slow the instability
of the nerwork learning caused by labels overlap.

Figure 11: The detection results of multiple grasping objects. The first column is the grasp outputs of corresponding RGB images for several objects. The last three columns are the maps for grasp quality, angle and width representing the opening and closing distance of the gripper. TABLE V: Network size comparison of different methods Author |  Parameters (Approx.) |  Time
---|---|---
Lenz [2] |  - |  13.5s
Pinto and Gupta [24] |  60 million |  -
Levine [44] |  1 million |  0.2-0.5s
Johns [45] |  60 million |  -
Chu [10] |  216 million |  120ms
Morrison [14] |  66 k |  3ms
Ours |  4.67 million |  5ms

###  VI-G Comparison of network parameter sizes

In Table. V, some comparisons of network sizes used for grasping predictions
are listed. Many works, such as [24, 44, 45, 10], contain thousands or
millions of network parameters. In order to improve the real-time performance
of the grasping algorithm, we developed a lightweight generative grasping
detection architecture, which achieves high detection acurracy and fast
running speed, and its network size of 4.67M is an order of magnitude smaller
than other methods.

###  VI-H Objects in clutter

To validate the generalization ability of the proposed model in clutter scene,
we use the model trained on the Cornell dataset to test in a more realistic
multi-object enviroment. The detection results are presented in Fig. 11.
Although the model is trained on a single object dataset, it is still able to
effectively predict the grasp pose of multiple objects. In complex scenarios,
the proposed model has better generalization ability to perform grasp pose
estimation for multiple objects simultaneously.

###  VI-I Failure cases analysis

During the experiment, it was found that although the proposed algorithm
achieved high detection accuracy, it still failed to detect some cases, as
shown in Fig. 12. For some objects in the Jacquard dataset with complex
shapes, our model does not work well. Furthermore, in the clutter scenes,
smaller objects among multiple objects are often missed by the model, and the
detection quality of the model for large boxe is not good as well. However,
these shortcomings can be addressed by increasing the diversity of the
training dataset.

Figure 12: Failed detection cases with single and multiple objects.

##  VII Conclusion

In this paper, we proposed a Gaussian-based grasp representation to highlight
the maximum grasp quality at the center position. Based on Gaussian-based
grasp representation, a lightweight generative architecture with a receptive
field block module and multi-dimensional attention fusion network was
developed for grasp pose estimation. Experiments on two common public
datasets, Cornell and Jacquad, show that our model has a very fast inference
speed while achieving a high detection accuracy, and it reaches a detection
accuracy of 98.9 and 95.6 respectively on Cornell and Jacquard datasets.

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