## 5 Experimental Results
### Comparison Experiment  
To verify the feature constraint capability of the proposed DQN feature constraint visual servo under different noise environments, we conducted feature constraint experiments in three different noise environments and compared the results with those of the Kalman visual servo without feature constraints. We set the initial feature's state to \(S=[229.7,172.9,371.9,174.3,372.0,312.2,225.6,309.3]\), and the desired feature's state to \(S^{*}=[46.4,179.0,160.4,187.1,152.0,299.7,34.5,286.5]\). Meanwhile, in order to better compare the two methods' convergence effects, we set the VS mission area as (160-479) \(\times\) (120-359). **Test 1:** We introduced noise of varying intensities into the system and validated the servoing performance of both the Kalman-DQN visual servo and the Kalman visual servo under different noise conditions. In experiment text1, we set the system noise covariance to \(Q=0.9I_{48\times 48}\) and the observation noise covariance to \(R=0.01I_{8\times 8}\), respectively. As observed in Figure 10a,b, when the initial feature's state is within the feature constraint region, the proposed DQN feature constraint control is activated. The DQN module's control effectively compensates for the convergence of the visual servo, resulting in a relatively smooth trajectory within the feature constraint region compared to (b). In contrast, the Kalman visual servo in (b), lacking the compensation from the DQN module's feature constraint, exhibits weaker convergence performance due to the influence of noise on the Kalman estimator, leading to a relatively more curved trajectory. Comparison of (c,d) and (e,f) leads to the conclusion that our proposed visual servoing scheme has faster convergence and better spatial trajectory curves. Figure 10: Experimental results of Test 1. 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. **Test 2:** The spatial trajectories of the end-effector with camera and the image plane convergence trajectories when \(Q=4I_{8\times 48}\), \(R=0.04I_{8\times 8}\) are given in Figure 11. The results show that the overall image convergence trajectory and spatial convergence trajectory of our proposed method still outperform the Kalman visual servo without feature constraints due to the feature constraint compensation effect in the presence of increased noise, which further demonstrates the stabilizing property with robustness. In terms of convergence time, Figure 11c,d show that our method converges faster. **Test 3:** When increasing the noise setting to \(Q=9I_{48\times 48}\), \(R=0.09I_{8\times 8}\), as shown in Figure 12, due to the increased Jacobian matrix error in the Kalman estimation, there is a larger camera back-off in the workspace, which further increases the clutter in both the spatial convergence trajectory and the image plane convergence trajectory. However, in the face of the same noise, for our proposed DQN feature constraint visual servoing method, the image convergence trajectory, the spatial trajectory, and the convergence speed are superior to the Kalman visual servoing without feature constraint. Furthermore, experiments in different noise environments demonstrate that the localization results of the Kalman visual servoing without feature constraint change significantly even with slight variations in the noise covariance of \(Q\) and \(R\). When using the DQN feature constraint as an auxiliary to the Kalman visual servoing, our proposed DQN feature constraint method not only ensures the visibility of visual features, but also, in the presence of large dynamic noise, guarantees the robust stability of the convergence task. Figure 11: Experimental results of Test 2.