## 1 Introduction  
Visual servoing control technology represents a closed-loop approach that makes use of vision feedback information [1]. The visual sensors empower the robot to explore its workspace with high reliability and execute intricate tasks within unstructured settings. Therefore, robots integrated with visual servoing control technology are also widely applied in the fields of automatic driving [2], automatic drilling [3], and robotic services [4, 5]. In general, based on the different feedback information from the system, visual servoing can be categorized into position-based visual servoing (PBVS) [6, 7], image-based visual servoing (IBVS) [8, 9], and hybrid visual servoing (HVS) [10]. PBVS utilizes 2D image data to reconstruct the robot's pose relative to the environmental objects. The accuracy of the pose information is highly sensitive to camera calibration errors. Compared with PBVS, since IBVS directly utilizes 2D image information to construct a closed-loop control, it eliminates the pose reconstruction step, making the control scheme more concise. In contrast, HVS combines the control mechanisms of both PBVS and IBVS. Due to the concise control scheme of IBVS and being less sensitive to camera calibration error, it has gained much attention in the visual servoing field. In [11], the IBVS method was used to achieve camera window tracking control for a quadrotor drone. The C-IBVS method introduced in [12] improves the convergence speed by incorporating a classical proportional controller,which exponentially reduces the tracking error. In [13], the convergence time was reduced by incorporating fuzzy logic techniques into the IBVS method. The Sliding Mode Control (SMC) method was used in [14] to cope with the problems of external perturbations and parameter uncertainties in the system, which has already enhanced the stability and robustness of the IBVS. In order to solve the IBVS problems with physical constraints, Model Predictive Control (MPC) methods were proposed in [15; 16]. The above methods assumes that the target always remains within the camera's FOV and that the features can be detected during the entire servo process. If the visibility constraint problem in IBVS is not considered, the continuous feedback link of feature information may be interrupted or become an outlier. In practical applications, due to the camera's limited FOV, vision-based navigation [17], vision-based tracking and localization [18], etc., may all lead to issues of feature loss, which can lead to task interruptions and even cause unpredictable motion of the robot. Therefore, in practical vision servo applications, the FOV constraint of uncalibrated IBVS is an issue that needs to be considered. To prevent feature loss, numerous approaches have been proposed in recent decades. For example, motion path planning methods are used to constrain visual features within the camera's FOV. [PERSON] et al. [19] presented a virtual target-guided RRT algorithm that iteratively explores a scaled Euclidean space under unknown image depth to identify paths that comply with FOV constraints. However, motion planning requires establishing a corresponding robot workspace model and is dependent on the accuracy of camera calibration [20]. Further, ref. [21; 22] ensure FOV constraints by yet planning the camera's Cartesian path. In [23], the potential function (PF) method is used to constrain features in the image danger zone within the safe region. In [24; 25], the navigation function method is used to constrain image features within the camera's FOV safe zone. But for the potential function and navigation function methods, the construction of the corresponding functions in the image plane requires careful design to be suitable for the specific IBVS tasks. A control barrier function-based method was proposed in [26] to constrain the maximum deviation between visual feature coordinates and the image plane center, ensuring that the features always remain within the FOV.