# Simulation Model for Robotic Pick-Point Evaluation for 2-F Robotic Gripper
## 3 Simulation Model for Object Pick-Point Evaluation
### Robotic Gripper Force Controller  
To approximate the movement of a 2-F robotic gripper closing, the movement of both fingers is controlled by a P force controller. The reference value of the force controller is the  
Figure 5: Translation and rotation settings of the robotic gripper in ADAMS/View. Source: own.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter/Contact** & \(\mathbf{C_{LF\text{-}O}}\) & \(\mathbf{C_{RF\text{-}O}}\) & \(\mathbf{C_{O\text{-}G}}\) \\ \hline Normal force & Impact & Impact & Impact \\ \hline Stiffness (N/mm) & \(10^{5}\) & \(10^{5}\) & \(10^{5}\) \\ \hline Force exponent & 1.2 & 1.2 & 2.2 \\ \hline Damping (Ns/mm) & 5.5 & 5.5 & 10 \\ \hline Penetration depth (mm) & 0.001 & 0.001 & 0.01 \\ \hline Friction force type & Coulomb & Coulomb & Coulomb \\ \hline Coulomb friction & On & On & On \\ \hline Static coefficient & 0.86 & 0.86 & 0.4 \\ \hline Dynamic coefficient & 0.86 & 0.86 & 0.2 \\ \hline Stiction transition velocity (mm/s) & 100 & 100 & 100 \\ \hline Friction transition velocity (mm/s) & 1000 & 1000 & 1000 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Model contact parameters. Source: own.  
desired contact force between the finger of the robotic gripper and an object to be gripped, expressed in Newtons (\(N\)). The output of the force controller, which is limited by \([-lim,\,lim]\), is the robotic gripper closing speed, given in (\({}^{\circ}/s\)) since the joints are rotational. The output of the force controller is connected to the input ports of the ADAMS model. Both fingers of the robotic gripper are controlled simultaneously, multiplying the amount of output speed by (\(-1\)) for the right finger due to the clockwise direction of the joint's rotation. The control scheme is shown in Figure 6, and the full Simulink model is shown in Figure 7.  
For tuning the force controller, the Ziegler-Nichols method was used. Due to the settings of the controller (at the beginning, the P part must be large enough for the system to react quickly and, at the end, small enough not to cause any overshoot), a compromise was sought between the two values, which resulted in a slow closing of the gripper, but avoided the subsequent rapid response of the controller. Still, the closing velocity remained in the boundary of the actual gripper closing velocity. The parameters of the force controller are presented in Table 2. The problem with higher values of the P part of the controller occurs mainly after a longer grasping time, as the minimal change in velocity causes the object to slip out from under the robotic gripper. As noted by the [PERSON], [PERSON], and [PERSON] [26], the slipping problem may stem from the simulation tool itself. The issue can be contained to a certain extent but cannot be eliminated. An adaptive controller would allow changing the controller coefficients dynamically according to the current response, further minimizing the slipping of the object.  
\begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{1}{c}{**P Force Controller**} \\ \hline Gain & 0.08 \\ \hline Output limit & 50/\(-\)0.01 \\ \hline \end{tabular}
\end{table}
Table 2: Force controller parameters. Source: own.  
Figure 6: Force P-controller used to control the closing of robotic grippers’ fingers. \(F_{d}\) is the desired value of contact force between the robotic grippers finger and the object, and \(F_{act}\) is the actual contact force.  
Figure 7: MATLAB/Simulink control diagram. Source: own.  
In addition, because of the slip problem mentioned above, we set the condition that as soon as the controller reaches the set contact force, the lifting of the object is started. Otherwise, the object's slipping begins before it reaches its final height. Figure 8 shows the close-up of the contact force between the left robotic finger and the selected object.