## 2 Control Method
### Position-Rate Hybrid Teleoperation Control  
Figure 2 is a schematic of the proposed position-rate hybrid teleoperation control. The subscripts m, s, c, and d in Figure 2 represents the master device, slave robot, current, and desired, respectively. The position-based process recognizer outputs the corresponding subtask index based on the distance between the slave robot position and the desired position. With this result, the input space controller determines the input space (\(\alpha\)), and  
the control-mode selector determines the control mode (\(\beta\)) between the position and rate control.  
\[\dot{x}_{m}=diag(\alpha)(\beta\dot{x}_{(m,p)}+(1-\beta)\dot{x}_{(m,r)}), \tag{3}\]  
\[\dot{q}_{s}=J^{*}(\dot{x}_{m}). \tag{4}\]  
\(\dot{x}_{(m,p)}\in R^{(6\times 1)}\) represents the position controller, and \(\dot{x}_{(m,r)}\in R^{(6\times 1)}\) represents the rate controller. \(\dot{x}_{m}\in R^{(6\times 1)}\) is determined by the scalar value of \(\beta\) in the tables below to apply the corresponding mode between the position and rate control for each subtask. \(J^{*}\in R^{(7\times 6)}\) is the inverse of the Jacobian, and \(\dot{q}_{(s,d)}\in R^{(7\times 1)}\) is the desired joint velocity. Our teleoperation system assigned position and rate-control modes based on the corresponding subtask index using a predetermined \(\alpha\).  
We selected an advantageous control method from the corresponding subtask index among the two control methods to complete the MADMOFEM tasks. For example, because of the distance between the target position ( the position of the shaft or driver) and the initial position, we used rate control to approach the target quickly and switched to position control when the target was close, allowing the task to be completed accurately and safely.  
Predetermined input space vector \(\alpha\) and control mode \(\beta\) are listed in Tables 1 and 2. With the \(\alpha\) vector, the input space for the slave robot is determined and is also used for haptic rendering. If the corresponding value is zero, then the input space is ignored; otherwise, the input space is allowed. For example, in the C1 state, the operator must handle the master device in the yaw direction. Therefore, only the value of \(\alpha_{yaw}\) is set to 1.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \  
When the value of the Euclidean distance between the robot and the target in the direction where the input space is allowed is below the threshold, the state is converted to the next state. For example, because the input space in the yaw direction is only allowed in the C1 state when the yaw component of the target and the robot are below the threshold, it is converted to the next state, which is the C2 state. In the C2 state, the \(\alpha_{x}\) and \(\alpha_{y}\) components are equal to 1; therefore, when the Euclidean distance in the corresponding direction is below the threshold, the state switches to the C3 state, and proceeds to switch repeatedly until the final state is achieved.  
As the corresponding state is determined based on the slave and target positions, the algorithm has the disadvantage of not being available in an unstructured environment because it assumes that we know the location of the target. Therefore, in future work, we plan to improve the state conversion automatically by using vision-based deep learning that takes the egocentric view mounted on the end-effector as an input.