Very often in teleoperation of surgical robots, we discover that there is some degree of uncertainty in terms of locating critical time delays necessary to establish criteria sustaining stable and safe surgical regimes. Within the stable and safe regimes optimal performance indices and critical time delays combine to deliver a greater motion rhythm for the teleoperation of surgical robots. In this paper, we apply a bilateral controller of the modified wave variable (MWV) type to locate critical time delays maintaining stable and safe teleoperation of a specific surgical robot. The controller implemented additional wave impedance in the wave variable transformations in order to focus more closely on force tracking. The effectiveness of the proposed controller and locate dynamics of specific phenomena that align with the cumulative energy density required to operate the surgical robot are investigated. Firstly, the stability of MWV is investigated in detail. Then, the effect of additional wave impedance is discussed theoretically. Finally, experiments are conducted for three degrees of freedom master and slave manipulators to demonstrate the effectiveness of the MWV. The controller provides superior position and force tracking performance compared to the traditional wave variable-based method. The proposed method can improve position and force tracking errors between the master and slave caused by the communication channel time delay.

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