# Bilateral Teleoperation System with Integrated Position/Force Impedance Control for Assembly Tasks
## 5 Experimental Validation
### Experimental Results
#### 5.3.4 Statistical Experiments  
A statistical analysis was performed on the results of 10 replicate experiments for each method. In each experiment, the tasks and conditions were the same as described above. Figure 12 compares the biggest contact force in the X axis during inserting phase of different methods. Figure 13 shows the biggest contact force in the Z axis. Additionally, the success rate of task was also counted.  
The horizontal axis shows the number of experiments for each method, and the vertical axis shows the maximum contact force of the method in that experiment. Those red \"\(\times\)\" indicate that in this experiment, the remote robot stopped for protection due to excessive contact force.  
As observed from Figure 12, owing to the lack of position error correction mechanism, the position control shows the worst performance, with the average biggest contact force in the X axis of about 27.35 N. When implementing the assembly task by the proposed integrated position/force control method, the maximum contact force in the X-axis declined to approximately 10.49 N, which is less than that of the master-remote position control (decreased by 61%). This means the proposed method possesses the ability of position error  
Figure 12: The maximum contact force in the X-axis of the three methods in each experiment.  
Figure 13: The maximum contact force in the Z-axis of the three methods in each experiment.  
correction on human manipulation. The manual/automatic strategy based on impedance control performs the minimal average biggest contact force (about 6.12 N). However, it is only applicable to a specific known environment and needs to be redesigned or even failed when the environment changes [14]. In addition, method 1 possesses the maximum difference of square of 12.42, which was significantly higher than method 2 (2.37) and method 3 (9.09), indicating that the master-remote position control method was more susceptible to human The data in the \(Z\)-axis have similar results (8.55 N, 4.32 N, 5.4 N), but the force in this direction is small. This is because due to the use of the parallel gripper, when the force is too high, the loaded workpiece might slide in this direction. Additionally, both the automatic assembly and the proposed algorithm possess a similar high success rate (100%, 90%), while in the first, fourth  
and at the same time, it could dynamically adjust its posture according to the contact force, and the task success rate increased to 90%. In addition, it can be seen in Figure 15 that the integrated position/force control method had a lower collision risk than the method based on position control. There was a similar trend in the Z direction; however, the workpiece might slip due to insufficient clamping force, so the force in this direction is small. The reason for failure is the overshoot of the impedance correction due to excessive collision forces caused by large manual errors.  
In summary, it can be seen that the designed integrated position/force control method is able to guide the robot to work in unknown and complex environments. Compared with traditional impedance control, this method possesses higher control initiative; compared with position control, it possesses the property of position correction, which can suppress excessive contact force caused by human misoperation.