Stiffness and Impedance Control Using Lyapunov Theory for Robot-Aided Rehabilitation

In this paper, stiffness and impedance control concepts are used to solve position and force control for robot-aided rehabilitation. New asymptotic stability conditions are proposed using a suitable Lyapunov approach and based on the relationship between the dynamics of the robot and its energy. The efficiency of the proposed approach is tested on a planar 3 DOF robot-aided rehabilitation constrained to a circular trajectory. The robotic device is configured to be safe and stable in compliant motion in contact with the human arm. It is also designed to be adapted easily to different subjects for performing different tasks. Force and control parameters are tuned using a non linear optimization strategy for which the stability conditions are considered as inequality constraints. Simulation results show that the robot could guide the upper limb of subjects in circular movements under predefined model of the external force and prove the stability and the performances of the compliant motion control strategy.