## 3 Methods
### The Proposed FAGD-Net for Grasping Detection  
The architecture of the proposed grasping network, FAGD-Net, is depicted in Figure 2, the primary goal in designing of the FAGD-Net framework is to equip the grasping system with robust feature extraction capabilities to ensure high accuracy in grasp detection while keeping its architecture lightweight. FAGD-Net employs an encoder-decoder architecture to enhance contextual understanding from input data.  
Initially, a depth image undergoes feature extraction through a backbone network, which comprises only four down-sampling modules to ensure model lightweightness. Each down-sampling module consists of convolutional layers, batch normalization, and ReLU activation functions. The first down-sampling module utilizes a 9 \(\times\) 9 convolutional kernel, while subsequent modules use a 4 \(\times\) 4 kernel. These larger convolutional kernels offer broad receptive fields and rich feature representations. The size of the output feature maps is halved after each down-sampling module. Subsequently, features are further processed through the Residual Efficient Multi-Scale Attention (Res-EMA) module, which adjusts the importance of feature channels to highlight effective features while preserving precise spatial information within channels. In the Res-EMA module shown in Figure 2, \"g\" denotes the number of groups along the feature channel dimension after passing through conv block 2, \"X avg pool\" represents global pooling along the horizontal direction, and \"Y Avg Pool\" indicates global pooling along the vertical direction. Further details are provided in the subsequent sections.  
Following the encoder stage, we introduce the Feature Fusion Pyramidal Module (FFPM) between the encoder and decoder to enhance information utilization without compromising the receptive field. This effectively addresses potential oversights in grasp features during encoder down-sampling.  
Finally, the up-sampling module is utilized to expand and restore image dimensions. It consists of transposed convolutional layers, batch normalization, and ReLU activation functions, with the transposed convolutional kernel size set to 4 \(\times\) 4. Ultimately, the final grasp configuration is obtained through transposed convolution, completing the network's comprehensive grasp detection process, as described by Equations (5) and (6).  
Figure 1: The transformation of grasp configurations from the image space to the robot workspace.  
\[\left\{\begin{array}{l}F_{1}=f_{backbone}\Big{(}I_{depth}\Big{)}\\ F_{2}=f_{\text{Res}-EMA}(F_{1})\\ F_{3}=f_{FFPM}(F_{2})\\ F_{4}=f_{Up-sampling1}(F_{3})\\ F_{5}=f_{Up-sampling2}(F_{4})\\ \end{array}\right. \tag{5}\]  
where \(F_{1}\), \(F_{2}\), \(F_{3}\), \(F_{4}\), and \(F_{5}\) represent the feature maps after passing through the backbone (\(f_{backbone}\)), Res-EMA module (\(f_{\text{Res}-EMA}\)), Feature Fusion Pyramidal Module (\(f_{FFPM}\)), the first up-sampling block (\(f_{Up-sampling1}\)), and the second up-sampling block (\(f_{Up-sampling2}\)), respectively.  
\[\left\{\begin{array}{l}qualityMap=f_{trans\_conv}(F_{5})\\ AngleMap_{\text{sin}}=f_{trans\_conv}(F_{5})\\ AngleMap_{\text{cos}}=f_{trans\_conv}(F_{5})\\ WidthMap=f_{trans\_conv}(F_{5})\\ \end{array}\right. \tag{6}\]  
where \(f_{trans\_conv}\) represents the transposed convolution and \(F_{5}\) denotes the feature map output by the up-sampling block. Ultimately, the network generates feature maps of grasp quality, grasp angle, and grasp width.  
It is worth noting that we do not directly output the final grasping angle \(\theta\). Instead, we separately output \(\sin(2\theta)\) and \(\cos(2\theta)\) to eliminate discontinuities near \(\pm\frac{\pi}{2}\) and maintain  
Figure 2: The structure of the Feature-Augmented Grasp Detection Network (FAGD-Net).  
a unique mapping between \(\theta\) and the interval \(\left(-\frac{\pi}{2},\frac{\pi}{2}\right)\). Finally, the grasping angle is generated using Equation (7).  
\[\theta=\arctan\biggl{(}\frac{\sin(2\theta)}{\cos(2\theta)}\biggr{)}/2. \tag{7}\]