## 2 Method
### Control Algorithm
Unlike traditional joint-to-joint mapping approaches, which require significant mental effort from the user to actively control each robotic joint individually, this approach allows the user to command multiple robotic degrees of freedom (DoF) simultaneously by providing only a slight motion intention. In this study, we focus on the application of this control to _disconnected human-robot systems_. In such scenarios, users immerse into the remote environment of the robotic avatar, moving their bodies and controlling the robotic end-effector as if they were physically embodied in the avatar. For these cases, \(J_{hc}\) in (1) is zero, as human joints do not actively participate in the reaching task, unlike in _connected human-robot systems_. Additionally, \(J_{rc}\) is also null because robotic joints do not influence the pose of \(x_{c}\). In [17], the frame \(x_{c}\) is placed along the user's right shoulder. Its pose, as well as all other human joint values, can be directly measured using inertial measurement unit (IMU) sensors placed along the user's upper body. For this purpose, XSens MVN sensors can be employed, providing the pose of all joints in the user's biomechanical model, denoted as \(q_{h}\). In particular, the key sensors for this control strategy are those placed on the pelvis, trunk, and shoulder. During the control loop, the error \(e_{c}\) can be directly measured as the difference between the pose of the right shoulder relative to the human pelvis reference frame, from the starting time, \(t=0\) s, to the elapsed time. This formulation incorporates all residual motions of the user's upper body up to the shoulder within this term. Using the joint angles and body measurements, the Jacobian matrices can also be computed at each time step. The results presented in [17] demonstrate that, with this experimental setup, the user can incline and rotate their trunk and right shoulder to control virtual prosthetic arms with 3 DoFs, 4 DoFs, and 7 DoFs, attached to their digital twin, as well as a physical robot avatar system, to reach the target. The study highlights that it is possible to estimate the reaching error, and consequently the goal pose, based on the user's motion intentions. This enables robotic devices to reach the intended target without requiring the user to explicitly specify it. This approach allows the user to focus on the desired goal rather than directly controlling each robotic joint individually. Since the user plays a critical role in guiding control, the framework's effectiveness largely depends on their residual motion capabilities. This necessitates tailoring the control system to the user, by fine-tuning the weight matrices in the controller to match task requirements and the user's motion abilities. Another key factor is the choice of the frame \(x_{c}\). The placement of this frame can be adjusted to optimize the control strategy, aligning it more closely with the user's individual motion capabilities. While the control approach presented in [17] demonstrates promising adaptability across various systems and user conditions, it lacks validation through multi-subject tests to assess its usability and feasibility comprehensively. In this study, individuals with spinal cord injuries are the target population, focusing on their residual movements capabilities, that can affect both the weight matrices tuning and the placement of the \(x_{c}\) frame. Our goal is to adapt the control algorithm for robotic avatar systems to meet the specific needs of this population. We firstly aim at performing unimpaired multi-subjects tests, to evaluate the system's usability, accuracy, and performance in navigation and reaching tasks before and after tailored training sessions. Secondly, a pilot study with two SCI subjects is described, to test the training experimental protocol with them and to effectively verify whether they were able to perform the proposed tasks.