# A Robust Controller for Upper Limb Rehabilitation Exoskeleton
###### Abstract  
In this paper, a portable exoskeleton for the rehabilitation of upper extremities of three degrees of freedom (DOF) is proposed. With these degrees of freedom, the exoskeleton provides the movements of flexion-extension and abduction-adduction of the arm and flexion-extension of the forearm. A robust generalized proportional integral (GPI) controller for trajectory tracking to provide smooth movements for rehabilitation with the exoskeleton is proposed. This controller only requires output measurements and is robust against different types of disturbances. Simulation results are presented in the MSC Adams(r) software environment in co-simulation with Matlab-Simulink(r) to show the controller's performance against different types of disturbances. The results of a PID type controller are also contrasted with the results of the GPI controller. virtual prototype; upper extremities exoskeleton to rehabilitation; trajectories rehabilitation 2022121178202212178202212178202212178202212121782022121217820221212178202221212178202221212122122122122222222222222222222222222222222222222  
Some recently reported exoskeletons for upper extremity rehabilitation are listed below. The 6-REXOS is a 6-DOF (degrees of freedom) exoskeleton that provides the movements of: elbow flexion-extension, forearm supination-pronation, flexion-extension and radial-ulnar deviation of the wrist. It has four active rotational and two passive translational junctions to allow kinematic redundancy to the exoskeleton [8; 9]. MIT-Manus provides a robot-assisted therapy: a person sitting at a table puts the lower arm and wrist into a brace attached to the arm of the robot. A video screen prompts the person to perform an arm exercise such as connecting the dots. If movement does not occur, MIT-Manus moves the person's arm. If the person begins to move by themselves, the robot provides adjustable levels of guidance and assistance to facilitate the movement of the person's arm [10]. A shoulder exoskeleton of 6 DOF (two active and four passive) [11] has been developed that is composed of two spherical mechanisms, two sliding crank mechanisms, and a gravity compensation method. The exoskeleton uses linear series elastic actuators to implement impedance control at the exoskeleton-limb interface. Another example is a 5-DOF exoskeleton [12]; the shoulder was modeled as a 4-DOF joint by adding the shoulder elevation as a vertical movement, and the elbow was modeled as one DOF hinge joint. The authors performed direct and inverse kinematic analysis to verify that the proposed system was capable of reaching all points in the workspace. Cost is a design factor to consider, so a low cost robot has been proposed for upper extremity rehabilitation [13]; this robot has a mechanism to compensate for the effect of gravity so that the patient does not feel the weight of the robot. By changing the direction of the actuator in relation to the user, the robot can provide flexion/extension, abduction/adduction, horizontal abduction/adduction, internal/external rotation, and oblique lifting movements. Most shoulder rehabilitation devices are structures that are fixed to the ground and are not portable like exoskeletons. Table 1 presents a summary of some upper extremity rehabilitation devices. In this paper, a 3-DOF upper extremity robot configuration is proposed. With these DOF, the movements of flexion-extension and abduction-adduction of the arm and flexion-extension of the forearm can be provided (Figure 1). In patients with hemiplegia, the objective of the controller is to allow the rehabilitation to provide smooth movements that follow a desired trajectory for passive rehabilitation. To achieve this, the use of a robust generalized proportional integral (GPI) controller is proposed for trajectory tracking, which is compared with a PID type controller.