## 2 Materials and Methods
### Training Sessions  
The training program lasted 4 weeks and included 3 training sessions per week. Each session took 40 min and training days were scheduled on the same weekdays and time each week. The robotic training program was based on a high dose, high frequency [23], and task-oriented basis. During each training session, participants performed two 20 min work blocks of a tracking task separated by a 5 min rest period. Each block included 4 sets made up of 4 min of tracking, separated by a 1 min break. Only the participant's self-reported most affected limb was trained; the other limb was considered an untrained control limb. Using the WristBot, participants followed a Lissajous curve (figure-eight) by tracking a moving target on the computer screen. Participants were asked to follow the target to the best of their abilities. The tracking law of motion was the same as described in Equation (1) and both the size and the duration of the tracking were kept the same among training sessions. The tracking required movements in the space identified by flexion/extension and radial/ulnar deviation planes. Motors locked the supination and pronation plane in the neutral position. Since the size of the tracking figure was not meant to challenge the participant, it was scaled to a maximum of 80% of the individual's active ROM collected in T0 [24]. The active ROM was evaluated in 2 planes (flexion/extension, radial/ulnar deviation) and the smallest value was chosen to scale the figure. A greater ROM figure was not implemented for safety and to avoid end ROM while actively following a target trajectory. Given that the training protocol did not aim specifically at increasing ROM, the size of the figure did not change throughout the protocol and was only used as a safety standard before beginning the allotted training. However, before each session, participants underwent an active ROM test performed using the robot. This procedure was implemented for participant safety to ensure that ROM did not decrease with respect to T0 due to the unpredictable nature of MS symptoms (spasticity/rigidity) restricting joint motion [21]. Differently from the tracking performed during the assessment, the training task included assistive or resistive torques, accordingly to the online performance recorded. Figural error (FE, Equation (3)) was measured to characterize performance as the trajectory of the participant from the ideal figure-eight shape, regardless of speed. The training force was implemented as a virtual spring (_modulation_*_k_*_A_\(\theta\), see Equation (5)). The end-effector was pulled towards the moving target according to instantaneous distance (_A_\(\theta\)) and the selected spring stiffness. The stiffness of the spring determined the level of active muscle work required to perform the task more accurately. Opposingly, in the presence of resistive torques, the virtual spring would push the hand away from the target, effectively adding resistance to task completion. The evaluation of average figural error was completed every 3 laps/repetitions and was used to modify the level of assistance/resistance (_modulation_) according to the magnitude of deviation from the previous performance. The first three laps were performedwithout training force and used to assess the starting level of performance in terms of FE, required to compute _modulation_ for the following laps. The first 3 laps were excluded from the training analysis. Later, _modulation_ was adjusted for the following three laps as a computation of the mean FE and the assistance/resistance level of the previous laps, and was computed with Equation (4):  
\[modulation_{new}=modulation_{old}+a*\ (FE_{last3}\ -\ FE_{old})+b \tag{4}\]  
where \(modulation_{new}\) is the level of assistance to be adjusted to for the next 3 laps and \(modulation_{old}\) is the level of assistance from the previous 3 laps. \(FE_{last3}\) represents the participant's figural error from the prior 3 laps performed with the old value of _modulation_.