Problem statement: The assistance of person with limited ability of arm movement is necessary for rehabilitation reasons. This aid is required not only to cover the human performances of the arm in motion and force but also to have a strictly stable dynamics. In this study, we proposed a cooperative system between a disabled arm and a robotic manipulator to reach such objectives. Desired positions and contact forces were imposed by the disabled human whereas appropriate torques were applied by the manipulator to follow human intension. Approach: Various control strategies were proposed during recent years to solve position/force control problem. The impedance control concept was used in this study. A relationship between the dynamics of the robot and its energy was developed to derive stability conditions of the robotic system at the constrained motion phase using a suitable Lyapunov approach. Results: New sufficient conditions of asymptotic stability were developed. To prove the efficiency of the proposed approach, a prototype of a human arm coupled to cooperative constrained robotic manipulator was used. The simulation results showed the stability and the performances of the proposed approach. Conclusion: Results showed the possibility of their use in a real context of rehabilitation of injured and disabled people.
