## 2 Materials & Methods
### Float System Description
#### 2.2.1 Robotic Unit  
The robotic unit is in direct contact with the patient. It includes three elements: the actuated exoskeleton, a passive and polyarticulated arm and a mobile support with a telescopic column. The exoskeleton is the active part of the system and allows all the movements of the shoulder complex of the patient (according to design principle 1 about the arm). Two interfaces connect the patient to the exoskeleton: an orthopaedic but and an arm brace. The orthopaedic bust (Spinalplus, RO + TEN s.r.l., Milano, Italy) holds the patient to the base of the exoskeleton in a semi-rigid and repeatable manner. It also allows a shoulder strap to be removed if needed, which may be the case for patients with pain-sensitive shoulders. The second interface is an arm brace (Elbo 2.0, RO + TEN s.r.l., Milano, Italy) which connects the patient arm and forearm with the exoskeleton end-effector. This interface allows the transmission of movement from the exoskeleton to the patient in an ergonomic way (Figure 3). The Float exoskeleton is made of five rotational joints, with each degree of freedom representing a movement of the shoulder complex (Figure 3). The first two joints (J1 and J2) provide the two main movements of the shoulder girdle. The first joint allows the scapula protraction/retraction. The second joint allows the scapula elevation/depression. The last three joints represent the glenohumeral movements: horizontal abduction/adduction,  
Figure 3: Actuated exoskeleton kinematic structure of the Float system. (**A**), picture of the Float actuated exoskeleton with the orthopaedic bust and the arm brace and (**B**) the kinematic structure of the exoskeleton with the adjustable links. Figure 2: Float system overview. **Left**: The control unit; **Right**: The robotic unit (Exoskeleton, polyarticulated arm and mobile support). flexion/extension, internal and external rotation. They are assembled in a Euler spherical wrist configuration, also known as \"ZYZ\". This configuration, with respect to the Roll-Pitch-Yaw spherical configuration adopted in different rehabilitation exoskeletons, e.g., Harmony [9] and ANYexo [5], guarantees a better understanding of the contribution of each revolute joint rotation to the glenohumeral motion. Regarding J2, J3 and J4, the axis of rotation of the joint matches with the axis of rotation of the motor. They include a brushless DC motor equipped with integrated incremental encoder and a triplet of Hall sensors, and a Harmonic Drive gear unit. The output angular position is detected by a 20-bit magnetic encoder. Regarding J1 and J5, the axis of rotation of the joint does not match with that of the motor. For the first joint, a leverage system transmits the rotation from the motor to the output, while for the last joint the mechanism was made through two gear wheels. For J1 and J5, the joint position is sensed by means of a precision potentiometer (Table 1). The five degrees of freedom of the exoskeleton are sufficient to move the upper arm of the patient in the Cartesian space, guaranteeing the possibility to perform most of the activities of daily living (ADLs). Each motor is driven by means of a dedicated driver module, which manages the signals from the available sensors (fast shaft encoder, Hall sensors, joint angle sensor) and provides the needed power signals to the motor. Motor control is realized as a standard six-step drive, in which a pulse-width-modulated (PWM) voltage signal is sequentially applied to two of the three phase terminals of the motor stator, in order to generate a suitably rotating magnetic field. The duty cycle of the driving voltage signal can be controlled in order to modulate the driving voltage mean value. In the implemented low-level control scheme, said duty cycle value is computed in real-time by the algorithm for position control and friction compensation, which will be discussed in the following. Motor drive modules communicate with each other and the main control unit over a CAN bus line.