# Self-Recognition Grasping Operation with a Vision-Based Redundant Manipulator System
## 4 Simulation and Experiments
### Comparison with the Iteration Method  
The iteration method can also achieve pose transformation from the end-effector of the manipulator to joint angles and obtain a group of \(\theta\) values for grasping operation. However, it requires a proper initial configuration. If the initial configuration is not reasonable, no feasible solution can be reached. When the initial configuration is proper, a group of joint angles can be iterated and converged. In this part, the inverse solutions obtained with iteration method are compared with ones obtained with the ISPF method.  
In Table 2, 6 groups of initial configurations are listed to calculated joint angles with the iteration method. For the 1 st group, the inverse solution cannot be obtained due to an unreasonable initial configuration. For the other groups, inverse solutions can be converged. The manipulability of these solutions were calculated to compare the solution calculated by the ISPF method, which is shown in Figure 10.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{**Initial Configuration (\({}^{\circ}\))**} & \multicolumn{2}{c}{**Iteration Method**} \\ \cline{3-4}  & & **Reachable** & **Inverse Solution (\({}^{\circ}\))** \\ \hline
1 & \([-20,-20,0,0,0,0,0]\) & No & \\
2 & \([0,60,0,30,0,0]\) & Yes & \([-86.68,69.02,-35.71,46.48,-19.70,-28.69,41.19]\) \\
3 & \([10,10,10,10,10,10,10]\) & Yes & \([66.19,-69.73,-141.38,46.72,-23.00,-17.52,-24.06]\) \\
4 & \([-10,-10,-10,-10,-10,-10,-10]\) & Yes & \([78.50,-65.03,5.10,-46.85,-25.85,22.71,-170.49]\) \\
5 & \([-20,0,0,20,-20,0-20]\) & Yes & \([-116.24,71.07,45.38,47.45,-20.48,-17.05,-33.16]\) \\
6 & \([10,20,30,40,30,20,10]\) & Yes & \([-84.77,70.29,-41.19,46.68,-18.00,-29.38,44.80]\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Inverse solution with iteration method under different initial configurations.  
Figure 10: Comparison of manipulability at different groups of initial configurations, obtained by iteration and ISPF methods.  
In Figure 10, the manipulability of each solution calculated by the iteration method is smaller than the solution calculated by the ISPF method at \(\varphi=260^{\circ}\). Although solutions can be obtained by the iteration method, they can hardly be optimal. For self-recognized grasping operation in unstructured environments, various constraints should be guaranteed. The introduction of manipulability makes the manipulator achieve singularity avoidance and joint limit avoidance, leading to better adaption than with the iteration method in unstructured environment applications. Besides, considering the limit of the unstructured environment on the workspace of the manipulator, it is convenient for the ISPF method to adjust feasible solutions achieving obstacle avoidance.  
With the experiment, the efficiency of the ISPF method in obtaining the optimal solution for self-recognition grasping operation was verified. Compared with the iteration method, the ISPF method requires no default initial configuration. All the feasible solutions can be calculated, and the optimal one can be selected by introducing an optimal factor. Additionally, it is conveniently programmed with a high computational efficiency, supporting self-recognized grasping, making it a better choice than the iteration method in achieving pose transformation.