## 2 Dual-User Operation of Remote Robot System with Force Feedback
### Single-User Operation (Remote Robot System with Force Feedback)  
Figure 1 illustrates the setup of single-user operation (remote robot system with force feedback). The system comprises a master terminal and a slave terminal [23]. Each terminal consists of two PCs connected through a switching hub. At the master terminal, one PC is linked to a haptic interface device (3D Systems Touch [24]) for haptic feedback, while the second PC is utilized to monitor the movements of the robot arm. At the slave terminal, one PC connects a web camera (manufactured by Microsoft Corp. (Redmond, WA, USA), with a video resolution of 1920 \(\times\) 1080 pixels) to monitor the robot arm's movement, while the other PC controls the industrial robot. The industrial robot comprises a robot arm, a force sensor mounted on the arm's flange, a robot controller, and a force interface unit. The force interface unit is used to connect the force sensor to the robot controller.  
At the master terminal, by manipulating the haptic interface device, a user can control the robot arm remotely. As in [23], the reaction force \(\mathbf{F}_{t}^{(\mathrm{m})}\) exerted on the haptic interface device at time \(t\) (\(t\geq 1\)) is determined as follows:  
\[\mathbf{F}_{t}^{(\mathrm{m})}=K_{\mathrm{scale}}^{(\mathrm{F})}\mathbf{F}_{t-1}^{( \mathrm{s})} \tag{1}\]  
where \(\mathbf{F}_{t-1}^{(\mathrm{s})}\) denotes the force transmitted from the slave terminal, and \(K_{\mathrm{scale}}^{(\mathrm{F})}\) represents a force mapping scale used to map forces between the haptic interface device and the force sensor of the industrial robot arm [23]. Additionally, because the maximum force that can be applied to the haptic interface device is 3.3 N [24], any calculated force exceeding 3.3 N is capped at 3.3 N. At the slave terminal, we use the same method as in [23] to determine the industrial robot's position vector \(\mathbf{S}_{t}\). The \(\mathbf{S}_{t}\) outputted at time \(t\) (\(t\geq 2\)) is computed as follows:  
\[\mathbf{S}_{t}=K_{\mathrm{scale}}^{(P)}\mathbf{M}_{t-1}+\mathbf{V}_{t-1} \tag{2}\]  
where \(K_{\mathrm{scale}}^{(P)}\) is a scaling factor for workspace mapping, \(\mathbf{M}_{t}\) is the haptic interface device's position vector transmitted from the master terminal at time \(t\), and \(\mathbf{V}_{t-1}(=\mathbf{S}_{t}-\mathbf{S}_{t-1})\) represents the moving velocity of the robot arm at time \(t\)[23]. Additionally, \(|\mathbf{V}_{t}|\leq V_{\mathrm{max}}\), where \(V_{\mathrm{max}}\) represents the maximum allowable movement velocity (\(V_{\mathrm{max}}=5\) mm/ms [25] in this paper) to ensure safe operation of the robot arm.  
To avoid instability phenomena, such as vibrations, we implement stabilization control with filters [25], originally proposed for single-user operation, for dual-user operation. Figure 2 shows one control loop of the enhanced stabilization control, which employs both  
Figure 1: Setup of single-user operation (remote robot system with force feedback).  
a wave filter and a phase control filter. The wave filter consists of a cross component and a coefficient \(b\), while the phase control filter includes \(W_{s}(s)\) and \(W_{m}(s)\)[26, 27].