## 6 Experimental Results  
The SMCSPO parameter values used in the experiments are listed in Table 3.  
Figure 8: Experimental setup. Figure 9: Video feedback. To verify the methodology, seven experiments were performed with SMCSPO under different scenarios. These experiments included: (i) tele-operated bilateral control of the end effector; (ii) estimation of the perturbation at the end effector of the master/slave; (iii) tele-operated bilateral control of the 2\({}^{\mathrm{nd}}\) link; (iv) estimation of the perturbation at the 2\({}^{\mathrm{nd}}\) link of the master/slave; (v) tele-operated bilateral control of the base; (vi) estimation of the perturbation at the base of the master/slave; and (vii) tele-operated bilateral control of the end effector and the 2\({}^{\mathrm{nd}}\) link at the same time. The master and slave devices are shown in Figures 7 and 8. These experiments were performed in real-time scenarios in which the operator (human) set the master manipulator in movement, and the slave manipulator moved in accordance with this trajectory as evaluated by SMCSPO. The trajectory profiles for the end effectors of the master/slave devices are depicted in Figure 10. The trajectory for the master device's end effector is presented as a red line, while for the slave device, it is shown as a blue line. It is evident that the slave's end effector follows the master's trajectory with only a very small degree of mismatch. It can also be seen that the trajectories of both of the end effectors attain a maximum value of 88.96 degrees at 18 s on the time scale. It is worth noting that the end effector of the slave has a workspace of 0-90 degrees. The relative errors of the trajectories of the end effectors of the master and slave manipulators are shown in Figure 11. It can be seen that maximum value of error between the master and slave trajectories was 0.94 degree at 157.71 s on the time scale. It is clear from Figure 11 that the error profile is very small, which shows the accuracy of the proposed method. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline \(K\) of base & 8 \\ \(K\) of 2\({}^{\mathrm{nd}}\) link & 250 \\ \(K\) of end effector & 25 \\ \(k_{1}\) & 39 \\ \(k_{2}\) & 507 \\ \(\varepsilon_{0}\) & 1 \\ \(c\) & 13 \\ \(e\) & 1 \\ \(\alpha_{3}\) (End Effector) & 4.08 \\ \(\alpha_{3}\) (2\({}^{\mathrm{nd}}\) Link) & 10 \\ \(\alpha_{3}\) (Base) & 2.58 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Design parameters. Figure 10: Master/slave trajectories for end effectors. The estimated perturbations for the master's and slave's end effectors are presented in Figures 12 and 13, respectively. The maximum value of estimated perturbation for the master system was 90.87 N-m at 178.01 s, whereas for the slave system, this was 1635.72 N-m at 148.016 s.  
It is evident from Figures 12 and 13 that the estimated perturbation corresponding to the slave system had a much higher value than that for the master device. The reason behind this is the hydraulic  
Figure 11: Error between the end effector trajectories for master and slave. Figure 12: Estimated perturbation of the master end effector. Figure 13: Estimated perturbation of the slave end effector. system of the slave device. The dynamical value of the slave system is 303.26, which is higher than the value for the master device, which is 1.35135. The profiles for the estimated perturbations were similar, but with opposing directions. Numerically, the normalized values for estimated perturbation lay within the ranges [0, 1] and [\(-\)1, 0] for the master and slave systems, respectively. The normalized values were calculated as follows. \[P_{norm}(Master)=\frac{a_{i}-\min(a)}{\max(a)-\min(a)},\ i=1\ldots N \tag{39}\]  
\[P_{norm}(Slave)=\frac{a_{i}-\max(a)}{\max(a)-\min(a)},\ i=1\ldots N \tag{40}\]  
where \(a_{i}\) is the \(i^{th}\) value of perturbation.