# Bilateral Teleoperation System with Integrated Position/Force Impedance Control for Assembly Tasks
## 5 Experimental Validation
### Experimental Results
#### 5.3.2 Manual/Automatic Mixed Control Strategy Based on Cartesian Impedance Control  
In the mixed manual/automatic strategy based on Cartesian impedance control, the remote robot was guided by the operator once, close to the target point. Then, the robot accomplished automatic and compliant peg-in-hole assembly through the designed Cartesian impedance control algorithm. During the automatic inserting process, the end-position of the robot in the X and Z axis is adjusted through the impedance control. The remote robot gradually inserted the peg into the hole by position control until the contact force in the Y-axis exceeded the threshold (\(Fzs=20\)N). Based on experiments and related studies [14], in the impedance controller, the impedance parameters were set as \(m_{d}=1\), \(b_{d}=4\), and \(k_{d}=0\). The contact forces and position trajectory under the impedance controller are depicted in Figure 9. From the relationship between the force and the corresponding position in the initial stage of the automatic inserting, it can be derived that, as a force control method, the impedance control is capable of dynamically adjusting the command position according to the contact force that prevents excessive contact forces from occurring. The maximum contact force in the X-axis declined to approximately 5 N, and there were similar results in the Z-axis (maximum contact force of about 4 N). 3.3 Integrated Position/Force Control Method Taking the Demonstration Position as the Desired Position  
Distinguished from the traditional hybrid force/position control, in which the force control and the position control are in two non-interfering directions, the proposed integrated position/force control method took the demonstration position as the desired position. In the same motion direction, the robot executed the combination of operator control commands and local adjustment position commands. The operator's control commands reflected the user intent, and the local impedance force control loop performed position correction based on external contact forces. This enabled the combination of the operator's control intent and the impedance correction. In the experiment, the parameters of local impedance force control were still set as \(m_{d}=1\), \(b_{d}~{}=4\), and \(k_{d}=0\). Figures 10 and 11 show the position and contact force during assembly using the proposed integrated force/position control method. Figure 9: The contact force and the trajectory by manual/automatic mixed controller (**a**) in X axis; (**b**) in Z axis. Figure 10 describes the trajectory of the operator (tracker), the desired position, and the actual robot position in the X direction. As shown in Figure 10, at point A (T = 6 s), the end of the remote robot makes contact with the pipe. At this point, it can be observed that under the impedance adjustment, the corrected command position (blue line) and the actual position (orange line) were retracted to the center of the hole-compared with the operator's position (black line). It is more evident at point B (T = 12 s) that a strong collision with the circular hole was produced. It can be observed clearly that the operator's position deviated severely from the center of the circular hole and generated a huge collision force. However, under the adjustment with local integrated impedance-based control, the corrected commanded position and the actual position were pulled back toward the center of the circular hole (value = 0). Furthermore, as shown in area C of Figure 10, although the operator's demonstrated position significantly deviated from the hole position, the  
Figure 11: The contact force in the X direction by the integrated position/force controller. Figure 10: The position in the X direction by the integrated position/force controller. The blue background in the figure represents the geometry of the assembly hole. robot arm was still in the round hole, and no collision was created.