# Improving the Manipulability of a Redundant Arm Using Decoupled Hybrid Visual Servoing
## 4 Results and Discussion
### Case Study 2: Performance Analysis of Four VS Methods Using Setup 1  
In this section, the effective parameters during tracking 10 positions by four different VS methods are compared with each other quantitatively and the results are tabulated in Tables 1-3. According to Table 1, the DHVS method has a lower mean RMSE than PBVS and HVS, and the range of feature error in PBVS and the classical HVS is greater than that value in the DHVS. As a result, in the DHVS, the object is less likely to be missed from the camera screen than in the other two approaches. Not to mention that the DHVS method is quicker than traditional HVS, and needs fewer iterations to complete the same mission. Table 1 shows that the IBVS method not only has the smallest range of feature error, but also the smallest RMSE as compared to other approaches. Without a doubt, IBVS performs better in the image-plane if there is no singularity or local minima. However, the controller operates blindly in the Cartesian space (with the highest RMSE for location and orientation as shown in Table 2). Large camera motions are common in the IBVS approach. As shown in Table 2, in Cartesian space, the DHVS method performed better than IBVS and HVS, as one would expect. However, the mean RMSE amounts of position and orientation in the PBVS method were less than their counterparts in the other three methods. As a consequence, in Cartesian space, the PBVS method had the best results, followed by DHVS. Ultimately, the DHVS method indicates more optimised efficiency in the Cartesian space than IBVS and HVS (based on the amounts of mean RMSE shown in Table 2). Furthermore, DHVS outperforms PBVS and HVS in image-space (based on the amounts of RMSE and feature error ranges, shown in Table 1). In Table 3, a quantitative comparison of manipulability has been presented. When using the DHVS approach for VS, the mean of manipulability across the entire path is higher than when using the other three methods. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multirow{2}{*}{**RMSE**} & **Feature Error** & \multirow{2}{*}{**Iteration**} & \multirow{2}{*}{**Mean of Error**} & **Mean Standard** \\  & & **Range** & & & **Deviation of Error** \\ \hline IBVS & 0.0222 & \([-0.36,0.310]\) & 453 & 0.0152 & 0.0095 \\ PBVS & 0.0383 & \([-0.445,0.507]\) & 487 & 0.0204 & 0.0164 \\ HVS & 0.0273 & \([-0.448,0.486]\) & 624 & 0.0168 & 0.0141 \\ DHVS & 0.0258 & \([-0.439,0.443]\) & 587 & 0.0159 & 0.0112 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Performance of visual servoing methods in the image space. \begin{table}
\begin{tabular}{l c c c} \hline \hline \multirow{2}{*}{**Method**} & **RMSE of** & **RMSE of** & **Camera (or EE)** \\  & **Position (m)** & **Orientation (\({}^{\circ}\))** & **Travelled Distance (m)** \\ \hline IBVS & 0.036 & 9.43 & 0.942 \\ PBVS & 0.022 & 6.54 & 0.722 \\ HVS & 0.034 & 8.41 & 0.917 \\ DHVS & 0.031 & 6.89 & 0.834 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Performance of visual servoing methods in the Cartesian space. It stems from the fact that translation in \(X\)-axis and \(Y\)-axis of the camera velocities are computed directly from the image space, while the rest are computed from 3D reconstruction of the environment. Furthermore, as compared to HVS and PBVS, the object in DHVS is less likely to be lost from the camera FOV. This conclusion was reached by comparing the maximum feature error in Figure 6d to the one in Figure 6a,c, which is less. The larger the error, the more likely the feature lost from the camera FOV. According to Figure 7, DHVS (the blue path) has a shorter camera path than HVS (the purple path) and IBVS (the red path). To elaborate, the camera (or the robot EE) travelled 0.843 m distance in DHVS; however, this value is 0.942 m and 0.917 m in IBVS and HVS, respectively. In PBVS, the camera travelled distance is 0.722 m, which provides the most optimised Cartesian trajectory of the robot EE, as predicted.