# Visual Tracking Control of Cable-Driven Hyper-Redundant Snake-Like Manipulator
## 4 Experiment and Validation  
In this section, an experiment is implemented to validate the moving and controlling performances of CHSM based on the introduced visual tracking.  
The prototype platform used for the experiment is shown in Figure 7. The primary parameters are illustrated in Table 1. Moreover, the PID parameters \(K_{P},K_{I},K_{D}\) are selected as \(K_{P}=5,K_{I}=2,K_{D}=0.05\) in a comprehensive consideration both for rapid response and stability of each actuator. The displacement signal of cable collected by Quanser QUARC software from the linear magnetic encoder to PID controller and the reverse controlling signal are all aggregated and passed via the real-time platform Simulink/Matlab with a  
Figure 6: The control scheme of CHSM.  
sampling frequency at 100 HZ. The visual servo feedback referring signal is captured by the camera (attached on the end tubular structural unit) which is working in BGR color space and 30 HZ refresh frequency. HOG features perform better and are adopted in the next experiments.  
The experimental results of tracking target are shown in Figures 8-11, where the target is moving towards a random direction with a slowly increasing velocity earlier and then reduced to a normal level later. The tracking component can accurately capture the target in the visual field and driving the CHSM to adjust its pose (according to the Kinematics Equations (11)-(18)) to focus on the target, which means the target always appears at the center of the camera's perceived screen in every frame. In that case, the moving trajectory of CHSM's endpoint should be identical to the target as closely as possible. The CHSM's moving in the Y-axis is limited to a narrow range due to the scale adaptation of the tracking component. Figures 9 and 10 show the experimental result of the X-axis and Z-axis, respectively.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Description** & **Values** \\ \hline \(\lambda\) & Regularization parameter of ridge regression & 0.01 \\ \(\eta\) & Learning rate for updating correlation filter & 0.025 \\ \(N\) & Number of tubular units & 5 \\ \(D\) & Distance from endplate to universal joint & 12 mm \\ \(R\) & Radius of tubular structure & 33.8 mm \\ \(H\) & Length of tubular structure & 106 mm \\ \hline \hline \end{tabular}
\end{table}
Table 1: Some parameters selected in the experiment.  
Figure 8: The moving trajectory of target and endpoint of CHSM.  
Figure 7: The prototype entity.  
The subscript labels \(d,r\) represent the target and the CHSM's endpoint respectively and have the same meaning in the Figure 11.  
CHSM has a good tracking performance with the target except for a little delay. The absolute value of error has the same variation tendency as the target's moving speed which may be caused by the limited sampling scope of the tracking component.  
Figure 12 shows the recorded perspective from the camera when the target is moving dragged by a rope and four frames are selected as representatives. The target is detected and highlighted by a green bounding box which is nearly located in the center of the frames. When the target moves, the tracking component detects the target's new position and guides the CHSM to focus on the target so that the bounding box looks such as rooting on the center. The bounding box's deviation from the center has the same tendency as the error (shown in Figure 11).  
Figure 11: The result of error.  
Figure 10: The result of Z-axis.  
Figure 9: The result of X-axis.