## 5 Experimental Results
### Ablation Study and Real Application  
Previous studies [37] have shown that in complex motions involving large rotations and translations, robotic arm visual servoing tasks are prone to target features exceeding the camera's field-of-view (FOV). To validate the effectiveness of our proposed DQN-based feature constraint module in uncalibrated IBVS tasks, we designed a series of ablation studies in challenging scenarios to compare its performance with that of uncalibrated IBVS without the DQN constraint module.  
In this ablation study, the feature constraint region representing the camera's safe FOV is set to (80-559) \(\times\) (120-359). The initial and desired features we defined are as follows:  
\[S=[111.29,185.20,212.88,146.42,255.64,247.87,145.20,289.65]\]  
\[S^{*}=[372.82,163.67,520.18,163.07,524.10,303.29,374.52,302.60]\]  
Figure 12: Experimental results of Test 3. The 1 st and 2 nd columns show the results obtained using our visual servoing based on DQN and Kalman visual servoing without feature constraint, respectively. (**a,b**) show the convergence trajectories, (**c,d**) illustrate the convergence errors, and (**e,f**) depict the end-effector trajectories, all when different features are constrained, respectively.  
As shown in Figure 13a,c,e, under the unconstrained visual servoing control, some features exceed the camera's FOV due to the extended convergence motion path, leading to non-convergent errors and oscillations in the spatial convergence trajectory. In contrast, Figure 13b,d,f demonstrate that our proposed DQN module successfully constrains all image features within the predefined safe FOV of the camera and achieves fast and stable convergence within the specified feature error tolerance, while also maintaining a smoother spatial convergence trajectory. This indicates that in uncalibrated IBVS tasks involving complex motion paths, image features may approach the FOV boundary or even exceed it, potentially affecting system convergence due to singularities in the feature-to-motion mapping matrix. However, our DQN-based feature constraint module in uncalibrated IBVS effectively addresses this challenge, ensuring the system's convergence.  
In order to verify the feasibility of our proposed method in practical applications, we applied the method to the task of assisted localization of a robot grasping an object, in which the experimental localization objects are randomly placed, and the Yolov8-pose object pose detection model is used to detect the actual objects as targets. The bottle cap object with the highest confidence in the first frame is selected as the target for localization  
Figure 13: Ablation study of the proposed DQN-based feature constraint IBVS method and unconstrained IBVS. (**a,b**) show the convergence trajectories, (**c,d**) illustrate the convergence errors, (**e,f**) illustrate the end-effector trajectories with an eye-in-hand camera.  
and grasping during real-time detection. The object localization point feature is inferred in real-time and feedback to the DQN-based IBVS controller. The object localization and grasping when the manipulator is at the initial position and the desired position are shown in Figure 14a,b.  
From the results of feature trajectory plots in Figure 14c, it is evident that with our proposed visual servoing method, the DQN feature constraint module can promptly make compensating corrections to the output of the IBVS controller. This enables the control of the manipulator to effectively draw the point features back into the visual servoing (VS) task area. Figure 14d,e illustrate that the feature convergence time of the DQN-based visual servoing is notably shorter. Additionally, the spatial trajectory of our method exhibits greater smoothness. In the robot grasping phase of visual servoing, the proposed method manages to identify a relatively ideal grabbing position. Consequently, these results demonstrate the effectiveness of the proposed method in practical robotic applications.