## 2 Dual-User Operation of Remote Robot System with Force Feedback
### Experiment Results for Clarifying Mechanisms  
Figure 6 shows the average of average force magnitude and average of maximum force magnitude at robot arm 2. Additionally, the figure shows the 95% confidence intervals.  
Figure 5: Plane view showing arrangement of the wooden stick, wooden blocks, and paper blocks.  
From Figure 6, we find that when the delay for one user is 0 ms and the delay for the other user increases, both the average force magnitude and the average maximum force magnitude tend to increase. In other words, the force exerted on the object rises as network delays become larger. A similar trend is observed when the delay for one user is 50 ms, 100 ms, or 200 ms. This indicates that as network delays increase, it becomes more challenging for users to operate the remote robot effectively. Additionally, the figure shows that when the total network delay is the same, for example, in the network delay combinations (0, 200), (50, 150), and (100, 100), the average force magnitude and the average maximum force magnitude are almost identical. This is because, despite the challenges faced by the user with the larger network delay, the user with the smaller delay can operate the remote robot more easily and assist the other user. As the smaller delay increases, it becomes more difficult for that user to control the robot, while the larger delay decreases, making it easier for the other user to operate the remote robot. Therefore, when the total network delay is the same, the average force magnitude and the average maximum force magnitude remain nearly identical.  
We conducted a \(t\)-test to verify whether there are significant differences among different network delays. Figure 7 shows the results of the \(t\)-test between combinations of network delays (please note that the cells in blue color represent the combinations of network delays. The first value represents network delay 1, and the second represents network delay 2). Each cell contains two values: the upper value represents the \(p\)-value for the average of average force magnitude between network delay combinations, and the lower value is the \(p\)-value for the maximum force magnitude. For clarity, we have highlighted cells in which there is no significant difference (i.e., when at least one of the two \(p\)-values is greater than 0.05) in yellow.  
From Figure 7, we observe that at least one \(p\)-value is smaller than 0.05 when the difference between the total network delay (i.e., the sum of network delay 1 and network delay 2) becomes large. However, when the total network delay is the same, both \(p\)-values exceed 0.05. This suggests that there is no statistically significant difference between these pairs of network delays. In simpler terms, the force of robot arm 2 is nearly identical when the total network delay is the same. Therefore, even though the force applied to each of the two dual-users may vary due to different network delays, the force of robot arm 2 remains the same. This observation can explain why the user with the shorter delay can support the other user.  
Figure 6: Average of average force magnitude and average of maximum force magnitude.  
Figure 7: Results of \(t\)-test between combinations of network delays.  
We further confirm the above results by grouping the averages with the same total network delay in Figure 8. It is evident that the force remains nearly identical when the total network delay is consistent. As previously mentioned, despite the challenges faced by the user with the larger network delay, the user with the smaller delay can operate the remote robot more easily and assist the other user.  
Furthermore, we also carry out subjective assessment to confirm the effect of dual-user operation by comparing single-user operation and dual-user operation for cooperative work in remote robot systems with force feedback. The assessment results also illustrated that dual-user operation outperforms single-user operation [29].