## 6 Conclusions  
The findings of this study highlight several promising applications for the proposed system. The results demonstrate that the new control algorithm effectively leverages residual upper-body motions to control an external device with a higher number of degrees of freedom (DoFs). Moreover, the algorithm accurately estimates the target to be reached, as evidenced by the convergence of both errors, \(e_{e}\) and \(e_{c}\). Post-training analyses also reveal that residual motions become less pronounced, indicating that subjects learn to perform tasks more efficiently over time. These preliminary results suggest that this control strategy can assist the SCI population in operating assistive devices, such as a humanoid avatar, by leveraging their residual motion capabilities. For instance, a slight motion of the upper arm can be sufficient to command a robot to move toward an object the user intends to grasp. The learning process observed is encouraging, with indices computed after the training sessions often outperforming those obtained beforehand. While the perceived workload is generally moderate, there is room for improvement in system usability. Future studies could explore adapting the control framework by positioning the user's reference frame, \(x_{c}\), on alternative body parts, such as the shoulder, depending on the subject's characteristics and level of impairment. This approach could expand the applicability of the system to a broader range of individuals with varying degrees of injury. Finally, experiments with the real robot Alter-Ego and additional participants are necessary to validate the system further and strengthen statistical robustness. Although the virtual environment has provided the opportunity to test the experimental protocol across different scenarios and setups, we aim to test the same protocol with a real robot. Since the control algorithm and the robot's kinematics remain unchanged, a similar success rate and performance to that observed in the virtual case can be expected. However, a different perception by the subjects, particularly in terms of usability and questionnaire responses, can be anticipated. From a perceptual standpoint, a real robot physically reaching the desired object, as opposed to a simulated one, may enhance the perceived potential of this system for real-world applications within the SCI context. To sum up, the results confirm the effectiveness of the proposed approach and suggest that we are on the right path to enhancing assistive technologies for individuals with SCI. Conceptualization M.C. and A.B. ; methodology G.G. and M.G.C. ; software M.F. and A.F. ; validation A.F. and M.C. ; formal analysis A.F. ; investigation A.F. ; resources A.M. and A.B. ; data curation A.F. ; writing--original draft preparation A.F. and M.F. ; writing--review and editing A.F., M.F., M.G.C. and M.C. ; visualization A.F. and M.F. ; supervision A.B. and M.C. ; project administration M.C. and M.G.C. ; funding acquisition M.G.C., A.B. and M.C. All authors have read and agreed to the published version of the manuscript. This work was carried out within the framework of the project \"RAISE-Robotics and AI for Socio-economic Empowerment\" and has been supported by European Union-NextGenerationEU. Funded by the European Union-NextGenerationEU. However, the views and opinions expressed are those of the authors alone and do not necessarily reflect those of the European Union or the European Commission. Neither the European Union nor the European Commission can be held responsible for them. This work was supported by the Italian Ministry of Research, under the complementary actions to the NRRP \"FitMedRob-Fit for Medical Robotics\" Grant (# PNC0000007). This study was approved by the Institutional Review Board (code CE IBRIS protocol-N. 2022/52 approved on 22 September 2022) and it conformed to the ethical standards of the 1964 Declaration of Helsinki. Informed Consent Statement: Informed consent was obtained from all subjects involved in the study.