## 2 Method and Principle  
To address the challenge of locating anchoring holes in coal mine roadways, a visual positioning system for anchoring holes is constructed in this study, and a monocular-vision-based method for visual positioning is proposed. As illustrated in Figure 1a, the proposed visual pose measurement system for anchor holes on the steel belt comprises three components: an anchor-drilling robot, a steel belt, and a pose measurement unit. The anchoring holes are circular and uniformly distributed along the steel belt, with the centerline parallel to the long edge of the steel belt. Images of the anchoring holes captured by a monocular camera typically appear elliptical; however, due to the proximity of the camera to the steel belt and the small angle between the camera's optical axis and the normal vector of the anchoring holes, these can generally be approximated as circular holes. This allows for the fitting of circular holes to determine the center coordinates of the anchoring holes. As depicted in Figure 1b, the pose measurement unit used for the anchor holes consists of a camera bracket, an industrial camera, and three laser pointers, all mounted at the end of the manipulator of the anchor-drilling robot. The three laser pointers are arranged around the camera bracket to project laser spots onto the coal wall of the roadway. The industrial camera is centrally positioned within the camera bracket to capture images of the roadway's coal wall featuring spot and steel belt characteristics. The external parameters between the camera and the three laser pointers can be calibrated using a total station. Since the optical axis of the camera was parallel to those of the laser pointers, the coordinate systems of the camera and the laser pointers shared the same orientation. It is only necessary to measure the coordinates of the camera's optical center and the laser pointers in the total station's coordinate system. The calibration of the camera and laser pointers can then be completed through coordinate transformation. These images are then transmitted to the industrial computer via a network cable. The industrial computer determines the pose of the steel belt anchor holes within the camera's coordinate system by executing a program based on the visual positioning method presented in this paper. The principle of the visual pose measurement system used for anchor holes on the steel belt is illustrated in Figure 2. During operation, the industrial camera captures images of the coal wall of the roadway, which includes three laser spot features and the features of the steel belt anchor holes. The image processing method identifies the centers of the laser spots (denoted as \(R_{i}^{\prime}\), \(i=1,2,3\)) and the centers of the anchor holes on the steel belt (denoted as \(H_{j}^{\prime}\), \(j=1,2,\ldots\)) within the image's coordinate system \(Oxy\). Subsequently, the coordinates of the three laser spots on the coal wall (denoted as \(R_{i}\)) within the camera's coordinate system \(O_{C}x_{C}y_{C}z_{C}\) are determined using a visual imaging model based on the known relationship between the camera and the three laser pointers. This allows for the calculation of the normal vector \(n_{W}\) of the coal wall plane \(S_{W}\) within the camera's coordinate system. Assuming that the steel belt is approximately coplanar with the roadway coal wall, the rotation matrix \(R\) of the steel belt anchor hole's coordinate system \(O_{H}x_{H}y_{H}z_{H}\) relative to the camera's coordinate system \(O_{C}x_{C}y_{C}z_{C}\) can be derived. Finally, the translation vector \(t\) of the steel belt anchor hole's coordinate system \(O_{H}x_{H}y_{H}z_{H}\) relative to the camera's coordinate system \(O_{C}x_{C}y_{C}z_{C}\) is determined by identifying the intersection of the line from the camera's optical center \(O_{C}\) through the image coordinates \(H_{i}^{\prime}\) of the steel belt anchor hole center with the coal wall plane of the tunnel.