## 5 Experimental Results
### Features Constraint Validation  
In order to validate the effectiveness of the feature constraints in our proposed DQN feature constraint scheme, two sets of experiments are conducted and described in detail in the following sections.  
**Test 1:** In this section of the experiment, the initial image features were set outside the VS mission area, in which the VS mission area is defined as (80-559) \(\times\) (120-359). To verify the scalability of the proposed feature constraint control, experiments were conducted using two different initial feature states (positions) within the feature constraint area. The experimental results are presented in Figure 8a,b, demonstrating that the DQN feature constraint control scheme effectively constrains the features, whose initial states are within the feature constraint region, to the VS mission area. Additionally, the constraint curves exhibit a relatively straight trajectory. From Figure 8c,d, it can be observed that in the DQN constraint control phase, the error convergence curves of the four features in the longitudinal direction are relatively smooth, with error values decreasing between 0 and 16 iterations. This result further indicates that the proposed DQN constraint control effectively handles the feature constraint task without compromising the convergence of visual servoing adaptivity. The 3D trajectory of the manipulator end-effector equipped with a hand-eye camera in Cartesian space is illustrated in Figure 8e,f. It can be observed that after the feature constraint action at the initial state positions, the overall convergence trajectory remains relatively smooth.  
Figure 8: When the VS mission area is (80–559) \(\times\) (120–359), the constraint control results for features at different initial states in the feature constraint area are shown. (**a,b**) present the convergence trajectories, (**c,d**) illustrate the convergence errors, and (**e,f**) depict the end-effector trajectories.  
**Test 2:** Verifying the feature constraint control capability of the DQN module during the servoing process. In this part of the experiment, the VS mission area was set to (0-559) \(\times\) (0-359) and (0-559) \(\times\) (120-480). Figure 9 illustrates the experimental results for two different sets of initial and desired feature states.  
As shown in Figure 9,b, the constraint control of the DQN module is activated to correct the IBVS trajectory if the features at different initial states move outside the safe region (VS mission area) during servo motion. In Figure 9c,d, it can be observed that within the intervals from 150 to 155 in (c) and from 10 to 20 in (d), the DQN module facilitates the convergence of the error between the desired and target features while maintaining feature visibility constraints. As can be seen in Figure 9e,f, the spatial convergence trajectory is more complicated when features appear to exceed the VS mission area during visual servoing. This can be considered as a large error in the feature-motion mapping matrix estimated by the Kalman mapping matrix estimator due to unknown environmental noise disturbances, which further leads to more complex control trajectories output by the visual servo controller. In this case, when features move beyond the VS mission area, the DQN module's feature constraint control is activated to pull them back into the VS mission area, ensuring the visual servoing task achieves convergence.  
Figure 9: Constrained features during the visual servoing convergence process in the VS mission area (0–559) \(\times\) (0–359) and (0–479) \(\times\) (120–480). (**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.