# Review of Advanced Medical Telerobots
## 1 Introduction
### The Critical Issue of Stability and Transparency of Telerobots
In this regard, the wave variable transformation (WVT) rooted in scattering transformation (ST) is the most commonly used approach in the literature [82] (see Figure 2). Using WVT, the transmitted force and motion signals are converted to wave variables. It has been shown that in the presence of unknown constant communication delay, WVT results in the passivity of the network. An important feature of WVT is that the transformation at the leader side is the inverse of transformation at the follower side. As a result, in the absence of communication delay (which would result in the passivity of the communication), the two transformations would cancel out each other, and thus no signal deviation would be imposed. However, in the presence of communication delays, the two transformations cannot completely cancel out each other, and this would result in a deviation of force and velocity tracking. WVT utilizes a tuning factor named wave impedance, which distributes the deviation from the reference between the force and velocity channels. A major problem with WVT is the sensitivity to variable time delays. Various versions of the WVT have been proposed in the literature (see [83] for a 2014 review), some of which are to make it robust to variability in the time delay, for example, using wave scaling, the intensity of which depends on the variability of time delay (the higher the variability, the lower the scale). Although the problem has been  
Figure 1: [PERSON]’s four-channel teleoperation (which becomes E-LFC when \(C_{5},C_{6}\
eq 0\)). addressed theoretically, this approach results in excessive deviation of tracking through the need for wave scaling. Wave scaling modifications do not tolerate delays that change abruptly (when derivation of delay is greater than unity). Another approach for stabilizing the telerobotic system in the presence of variable and unknown time delay, relaxing the assumption of slow changes of delay, is the time-domain passivity control (TDPC) approach [84]. This class of adaptive nonlinear stabilizer utilizes the concept of passivity observer (PO) and passivity controller (PC) (see Figure 3). PO observes the passivity condition of the system by monitoring the energy flow, and PC injects adaptive damping into the system to dissipate the extra energy. This approach was originally implemented in the energy domain; however, a modification of this approach has been implemented in the power domain to result in a smoother control behavior by distributing the dissipation over time. TDPC has been used as a one-port controller when it is placed only at the leader side, and it has also been used as a 2-port controller when two sets of PO/PC are placed on the two sides of the communication network to reduce the conservatism of the system. It should be noted that the one-port design of TDPC makes it possible to use that for the haptics system when the environment is virtualized, and this is another difference between TDPC and WVT. The above-mentioned approaches guarantee the stability of the system, assuming that the environment and the operator behave like inherently passive systems. However, in the context of rehabilitation or telerehabilitation, the behavior of virtual or human therapists would include the injection of mechanical energy into the system to empower the patient and make the task feasible. Energy injection is a non-passive behavior violating the main core assumption of conventional approaches. To address this problem, [PERSON] et al. has extended the design of the passivity-based stabilizers and designed a new class of nonlinear adaptive stabilization framework based on strong passivity theory (SPT), which does not require passivity of all included components [7; 85]. For this, the excess of the passivity of the user's biomechanics is identified and used in the design of two passivity-based stabilization frameworks of the mentioned family.