# A Telepresence System for Therapist-in-the-Loop Training for Elbow Joint Rehabilitation
## 2 System Overview
### Visually Shared Training Model  
The visually shared training model shown in Figure 2 was proposed for elbow joint rehabilitation based on the neuro-rehabilitation theory that states that the brain has the ability to reorganize through sensory input, experience and learning [29]. The visually shared environment provides patients with goal-oriented tasks that enable them to use their decision-making abilities. The coefficients of springs (\(K_{T}\) and \(K_{P}\)) and dampers (\(C_{T}\) and \(C_{P}\)) shown in Figure 2 can be selected according to the predetermined muscle strength assessment system [27]. In particular, increasing the stiffness and viscosity in the model can relatively reduce the position-dependent and velocity-dependent error between the motion of the therapist and the one allowed for the patient [16]. Also, the patient is allowed to make errors  
Figure 1: Schematic diagram of the rehabilitation platform. in tracking the target object while performing motor tasks, which has been proved to be an essential factor for motor learning [30]. Through the visually shared model, the motion of the therapist and patient are measured and mapped to the orange and purple objects which correspond to the movement of the therapist and the patient's elbow movements. The position of the green object is a position resulting from the two sets of spring and damper. The red target object represents the desired position the patient needs to reach. This position will change after the green object reaches it. In particular, the force generated by the therapist can be transferred to the patient for delivering training, while real-time force feedback can be provided to the therapist so they know the amount of force being applied to patients through two sets of mass-spring-damper models as shown in Equations (1) and (2):  
\[F_{T}=k_{T}\theta_{T}+c_{T}\dot{\theta}_{T} \tag{1}\]  
\[F_{p}=k_{p}\theta_{p}+c_{p}\dot{\theta}_{p} \tag{2}\]  
where \(k_{T}\) and \(k_{P}\) represent the coefficient of elasticity on therapist and patient sides, respectively, \(c_{T}\) and \(c_{p}\) represent the viscosity coefficient on each side, \(\theta_{T}\) and \(\theta_{p}\) represent the change in the spring's length, which is in accordance with the forearm flexion/extension angle of therapists and patients, and \(\dot{\theta}_{T}\) and \(\dot{\theta}_{P}\) represent the velocity of the spring's deflection. The \(\theta_{T}\) is calculated from the relative kinematics with the haptic device, and the \(\theta_{p}\) is measured with an inertia sensor (MTx sensor, Xsens, Enschede, the Netherlands) mounted on the forearm [28]. Moreover, the additional merits of the proposed visually shared model for realizing and appropriately adjusting of training strategies and the amount of kinesthetic guidance provided over the session are summarized as follows: (1) when the patient needs assistance, the therapist can provide assisting force through the training model and the force can be generated by exoskeletons. It is also an assist-as-needed strategy, which was proven to be more effective. During the assistive training, the robot guides patients while assisting them towards the correct path; (2) during the supervision of the therapist, the therapist can also provide extra resistive force which is generated by exoskeletons with an impedance controller. In this case, the exoskeleton may dissipate parts of the energy generated by the patient to make the task more challenging; (3) the platform provides a high transparency with the model. Here, the master (patient) and slave (therapist) sides of the proposed platform can be represented by a 2-port network model which is distributed at both ends, and it is important to keep the transparency. The relationship of these components in the 2-port model can be represented with a hybrid model [31], as shown in Equation (3):  
\[\left[ \begin{array}{c}F_{p}\\ -p_{T}\end{array} \right]=H\left[ \begin{array}{c}x_{p}\\ f_{T}\end{array} \right]=\left[ \begin{array}{cc}h_{11}&h_{12}\\ h_{21}&h_{22}\end{array} \right]\left[