# ODGNet: Robotic Grasp Detection Network Based on Omni-Dimensional Dynamic Convolution
## 3 Method  
### Grasp Representation  
In this paper, we study the planar grasp detection problem. The target object is placed on a plane. Firstly, the RGB-D image of the target object is captured by a depth camera, and then the image is fed into the grasp detection network after certain preprocessing steps, and finally, the network outputs the object's grasping configuration, which guides the parallel gripper to perform grasping. The focus of planar grasp detection is to predict the grasp configuration information from the input image. The classical grasp representation method is proposed in [4], which describes a grasp posture by an oriented rectangle. A grasp posture is represented as \(g=(x,y,\varphi,w,h)\), where \((x,y)\) denotes the coordinates of the center point of the grasp rectangular box; \(\varphi\) denotes the angle of the grasp rectangular box positively to the x-axis; \(w\) denotes the opening width of the gripper jaws; and \(h\) denotes the width of the fingers of the gripper jaws, depending on the gripper jaw type used. However, the rectangle representation method does not consider the grasping quality of each grasp rectangle, and also, \(h\), as a known variable, can be ignored. Therefore, a new grasp representation was proposed in [8], as shown in Figure 1a, defining the grasp configuration of the gripper in the robot coordinate system as  
\[g=(p,\varphi,w,q) \tag{1}\]where \(p=(x,y,z)\) is the position of the grasp centre point of the jaws, \(\varphi\) is the angle of rotation of the jaws, \(w\) is the opening width of the jaws, and \(q\) is the quality score of this grasp. In reality, grasp detection will not directly obtain the grasping configuration in the robot coordinate system, but will first obtain the grasping configuration in the pixel coordinate system. Shown in Figure 1b is the grasping configuration in the pixel coordinate system, denoted as  
\[\widetilde{g}=\left(\widetilde{p},\widetilde{\varphi},\widetilde{w},q\right) \tag{2}\]  
where \(\widetilde{p}=(u,v)\) is the centre position of the grasp in the pixel coordinate system; \(\widetilde{\varphi}\) is the angle with the horizontal axis of the pixel coordinate system, which takes the range of \(\left[-\frac{\pi}{2},\frac{\pi}{2}\right]\); \(\widetilde{w}\) is the width of the grasp in the pixel coordinate system, which takes the range of \(\left[0,W_{gripper}\right]\), where \(W_{gripper}\) represents the maximum opening width of the jaws; and \(q\) denotes the quality of this grasp, which takes the range of \(\left[0,\ 1\right]\). The higher the value of \(q\) is, the higher the success rate of this grasp. Finally, the grasping configuration \(\widetilde{g}\) in the pixel coordinate system can be transformed into the grasping configuration \(g\) in the robot coordinate system according to the corresponding transformation matrix:  
\[g=\underset{camera}{robot}T(\underset{pixel}{camera}T(\widetilde{g})) \tag{3}\]  
where \(\underset{camera}{robot}T\) is the transformation matrix that transforms from the camera coordinate system to the robot coordinate system and \(\underset{pixel}{camera}T\) is the transformation matrix that transforms from the pixel coordinate system to the camera coordinate system. In order to achieve an end-to-end grasp detection network, it is necessary to predict the grasp configuration of each pixel point in the image. We define a set of grasp configurations corresponding to all pixel points in an image as three grasp parameter maps \(G=\left\{Q,\Phi,W\right\}\in\mathbb{R}^{3\times H\times W}\), where \(Q,\Phi,W\in\mathbb{R}^{H\times W}\) represent the grasp quality map, the grasp angle map, and the grasp width map, respectively. The value of each pixel point in the three maps represents the value of \(q,\widetilde{\varphi}\) and \(\widetilde{w}\) at that point, respectively. Once the input  
Figure 1: Grasping configurations of the same object in different coordinate systems. (**a**) Grasping configuration in robot coordinate system. (**b**) Grasping configuration in pixel coordinate system.