## Materials and Methods
### The Test-Bench  
In order to investigate the performance of the AP under actual operating conditions, the \"Hardware-In-the-Loop\" (HIL) approach was adopted, based on the integration of the AP in a specific bench capable of emulating its interaction with the operator and with the subject on trial, as shown in Figure 2. An experimental bench, used in previous works on the same topic [42; 43], was prepared for testing several versions of the AP. An accurate analytical model of the whole system was derived. The simulations of the dynamic behavior of the model were aimed both at the design of the AP and its control, and at the definition of the most effective characteristics of the same experimental bench. Numerous analytical models of the human body in posturographic trials have been reported in the literature, with various levels of complexity [44; 45]. In such models, the subject's response may be considered as the sum of a passive and instantaneous part, strictly correlated with the body mechanical impedance, and an active part, due to the intervention of postural motor reflexes, taking place after a given latency period. By designing the HIL equipment, only the passive part of the response was considered. Noteworthy, it is impossible to practically emulate the active one, which is strictly subject-dependent. To represent the passive response in the case of large perturbations, multi-segmental modeling would be indicated, since the evoked postural response likely affects different body segments. Since in our posturographic trials the perturbations given to the back of the subject were of limited magnitude, thus producing small oscillations of the body in the sagittal plane at most, the observed response could be simulated in the equipment by a simple 1-degree-of-freedom (DoF) mechanical impedance, in which the body is modeled as a single link inverted pendulum rotating around the ankle joint axis and provided with viscoelastic rotational stiffness. The same considerations can be applied to the operator, who can be emulated in the equipment by a second 1-DoF mechanical impedance. Since the angular oscillations of both subject's and operator's bodies were small, in the model as well as in the test bench, they were considered and realized as linear translations, like the motion provided by the actuator integrated in the perturbator (see Figure 2). Figure 3 shows the CAD model and actual HIL equipment specimen, whose component details are reported in Table 1. The pneumatic actuator of the AP (11) and an impacted mass (8), which represents the subject, are placed on two independent plates, (12) and (7), respectively, which slide on linear guides (9) by means of carts (13) and are connected to the fixed frame by means of viscoelastic dampers (1), which respectively model the passive reaction of the operator and of the subject. The two valves  
Figure 2: (**a**) Configuration of a dynamic posturographic trial, \(\vartheta_{1}\) and \(\vartheta_{2}\) refer, respectively, to the oscillations of the operator and of the subject about the respective ankle joints; (**b**) modelling of operator’s and subject’s motion through linear translations \(x_{1}\) and \(x_{2}\). (2) are placed just above the cylinder in order to shorten the pipes and hence to improve the dynamic response of the actuator. The potentiometers (6) are linked in parallel to the viscoelastic dampers and are used to measure the absolute position of cylinder body and mass. The laser sensor (10) is fixed to the body of the cylinder and is used to measure the cylinder stroke. A load cell (5), along with its support (3), is fixed to the rod end and is integral with the target of the laser sensor (4) as well as with the striker (15) placed at the end of the perturbator. The dampers allow a limited motion of about 30 mm of the perturbator and of the stricken mass, and they can be regulated in order to adjust their stiffness and damping coefficients. The most important components of the perturbator are the pneumatic actuator and the two proportional valves.