# Control Strategies for Gait Tele-Rehabilitation System Based on Parallel Robotics
## 2 Materials and Methods  
### Gait Simulator  
The gait simulator employed in this work is based on the operation of two parallel manipulators capable of performing on-site walking. Its main goal is to induce lower limb movements on a user standing on his/her feet over the platform. As depictedin Figure 1, the platform is designed to enable independent 6-DOF movement of each foot, thus producing motions ranging from normal walking to arbitrary lower extremity movements, hence potentially contributing for the restoration of motor function in different clinical scenarios. An overview of the gait simulator is illustrated in Figure 2. It is composed of two Stewart-Gough Platforms (SGP), each comprised of six pistons, whose coordinated displacement moves the upper platform to the desired position. They are connected to the Oil Hydraulic Power Unit (OHPU), which is comprised of valves that regulate oil flow through hosepipes in order to increase or decrease pressure and thus produce piston displacement. The basic design of the SGP is inspired by kinematic and dynamic features of human walking. Thus, one fundamental condition concerns the platform displacement range on the sagittal plane, which must allow adequate step width. The workspace and the maximum output forces produced by the system are listed in Table 1. Regarding the actuators, hydraulic actuation composed of 12 pistons (6 for each platform) driven by a 3 kW power OHPU are controlled by proportional electronic valves. A linear potentiometer is attached to each piston to assess the actual displacement. Regarding the hardware/software architecture, three computational units allow the user (i.e., therapist) to control the gait simulator. First, the Base Station Unit (BSU) is composed of a \"local\" Personal Computer (PC) with a Graphical User Interface (GUI) application, which serves to set up the platform operation mode, and an internet-based communication software that establishes communication with a \"remote\" PC or Remote Unit (RU) for tele-rehabilitation purposes. Second, the Wearable Sensing Unit (WSU) is based on wireless inertial sensors (3 space, Yost Technology, Ohio, USA) that allow the acquisition of the patient or therapist movement. Third, the microcontroller-based Control Unit (CU) implements a local closed-loop control of piston displacement. Either the BSU or the RU (i.e., local or remote PCs) may be used to acquired movement data from wireless inertial sensors. Figure 1: Gait simulator based on two Stewart–Gough platforms. During therapy, a user stands on both platforms, while a therapist supervises the system operation. Several safety measures have been implemented to protect the patient. A schematic describing the elements presented in this figure is provided in Figure 2.  
In order to evaluate the system tele-rehabilitation capabilities between users in different locations, possibly distinct countries, a specific software was developed. In particular, an internet-based software enables the interconnection between the BSU and a RU using TCP/IP connectivity. Through that connection, a therapist may, for instance, obtain real-time information from ongoing therapy, as well as send direct commands to control the robotic device. In this case, time delays and packet loss involved in internet communication may lead to instability. This issue is particularly important, since communication tests were done between Montpellier, France; Brasilia, Brazil; and the gait simulator located in Lima, Peru. Each parallel manipulator composing the system, referred to as left \(l\) and right \(r\), has one fixed base and one mobile platform onto which the user stands. The coordinate systems for the fixed base and the mobile platform are defined as \(G_{b}\) and \(G_{p}\), respectively, as depicted in Figure 2, and the \(G_{p}\) origin coincides with the foot median position. From a