# Multi-Layered Interactive Target Guidance with Visual Safety in Convex-Shaped Obstacle Environments
## 5 Verifications
### Comparison Between Cases with and Without the Safety Layer  
Finally, a simulation is conducted to demonstrate the benefits of using a multi-layered control structure. As shown in (62), obstacles are approximated as spheres in the planning layer. By making the spherical approximation sufficiently conservative, it is sometimes possible to maintain visual safety even without the safety layer. To eliminate the effects of this approximation, the obstacles are limited to spheres.  
The velocity of the object, \(v_{o}\), generally follows \(v_{o}=[-1.9\ 0\ 0]^{T}\), but as in the previous cases, it is adjusted by the control barrier function to avoid collisions. The parameter \(v_{0}\)  
Figure 9: Guarding task result. (**a**) Trajectories of the camera robot and target; (**b**) Distance \(\|p_{uw}-p_{task}\|\); (**c**) Value of \(h_{fov}(x_{pe})\); (**d**) Distance between each obstacle and the line of sight.  
satisfies condition (43) of Proposition 3, making it ideal for the safety layer. This setting with the initial position of the target and the obstacles as shown in Figure 10a creates a challenging situation for the camera robot to guide the object to the target location, as the target object moves around the spheres. As a result, the guiding task fails in this simulation. The camera robot's objective is the guiding task, and two types of simulations are performed. The first applies the nominal controller of (20) directly to the camera robot without using the safety layer, relying solely on the planning layer. The second applies the proposed method, using both the planning layer and the safety layer.  
Figure 10a,b show the results when the safety layer is not used. From Figure 10a, it can be observed that the camera robot attempts to guide the object to the target location by passing as close as possible to the obstacles. On the other hand, in Figure 10b, it can be observed that around 1.5 s, the distance between the line of sight and the obstacle becomes 0. In other words, the camera robot got too close to the obstacle, causing occlusion of the target object.  
Figure 10c,d show the results when the safety layer is applied. From Figure 10c, it can be observed that the camera robot maintains a distance from the obstacles. Additionally, Figure 10d shows that the distance between the line of sight and the obstacles is always kept greater than 0. This demonstrates that by adding the safety layer, the visual safety can be ensured.  
From these simulations, it is evident that interactive guidance can fail due to the target object, the camera robot, and the obstacles, as well as the motion of the target object. However, it was confirmed that the safety layer ensures at least the visual safety.  
Figure 10: Comparison between cases with and without the safety layer. (**a**) Trajectories of the camera robot and target without the safety layer; (**b**) Distance between the obstacles and the line of sight without the safety layer; (**c**) Trajectories of the camera robot and target with the safety layer; (**d**) Distance between the obstacles and the line of sight with the safety layer.