## 3 Experiments
### Experimental Protocol  
The experimental protocol, summarized in Figure 2, consists of multiple phases and lasts up to 90 min. Although real-world experiments can be performed using the physical Alter-Ego humanoid robot, we conducted this study in a simulated environment with the robot's virtual twin. This choice ensures a safer, more cost-effective testing process, accelerates development, and provides versatility for various applications, as discussed in  
Figure 1: Experimental setup with the subject wearing XSens sensors and looking at the screen ahead. In (**a**) the setup for the unimpaired subject, while in (**b**) the setup for the pilot study with SCI subjects. [PERSON] et al. [20]. Furthermore, the simulation code can be directly deployed on the real robot without modifications. Too meet SCI subjects' needs, we conducted the experiments for all subjects (included the calibration phase) in a seated position. The protocol begins with sensor placement and calibration, followed by a one-minute free exploration (FE). During this phase, participants freely control the robot in the virtual environment using upper-body movements, learning that the system allows simultaneous control of the robot's base and right arm. The study then advances to a test phase with two assessments, referred to as **Test 1** and **Test 2**, focusing on navigation and reaching tasks. * **Test 1** (Figure 3a): Participants are given 5 min to guide the robot to three targets. The first two targets are on the floor, requiring navigation using the robot's base, while the third target is accessed using the robot's end-effector. The optimal strategy involves aligning the robot's base with the floor targets and using the end-effector to touch the center of the final target. * **Test 2** (Figure 3b): This more complex scenario evaluates the participants' ability to interact with everyday objects. Here, they must use the robot's end-effector to reach a red glass placed on a table. As evidenced by the metrics discussed in the previous section, **Test 1** focuses on providing quantitative measures for system analysis, whereas **Test 2** offers a comprehensive qualitative overview. After the initial tests, participants proceed to a training session designed to teach control strategies through five progressive sub-phases (Figure 4), promoting a step-by-step learning. Figure 4: Schematic representation of the training sequence. Figure 3: Simulated virtual environments featuring the three targets for **Test 1** (**a**) and the everyday objects for **Test 2** (**b**). The first sub-phase introduces control of the robot's base rotation around the vertical Z-axis using the participant's right arm. By rotating their arm along its longitudinal axis, participants learn to rotate the robot base clockwise (\(-90^{\circ}\), right) and counterclockwise (\(+90^{\circ}\), left), as shown in Figure 4(a). In the figure, we represent with the red arrow the residual motions performed by the user, while the yellow arrow indicates the corresponding robotic motions. As observed, at the end of each training sub-phase, once user is satisfied with the robot's achieved position, he returns to his target posture, bringing the robotic joint velocities to zero. Figure 5: Frames highlighting the training sessions. Human motions are shown alongside the corresponding robot movements across the three training sessions. In (**a**), the sequence of motions required to rotate the robot, in (**b**) the motions to move the robot forward, and in (**c**) the motions to raise the robotic arm. The second sub-phase focuses on controlling the robot's forward along the X-axis. As depicted in Figure 5b, participants move their right upper arm forward to guide the robot along a linear trajectory. The third sub-phase introduces control of the robot's end-effector. By moving their right upper arm along the Z-axis and Y-axis, participants can raise the robot's arm, as shown in Figure 5c. The fourth step combines the strategies learned in the second and third phases.