Robust control of a cable-driven rehabilitation robot for lower and upper limbs

In this research, a redundant cable-driven robust rehabilitation robot has been proposed for helping and automating the proper function of the patient's lower and upper limbs in the presence of uncertainties, disturbances, noise, and time delay using a new control algorithm to derive the best tracking with the least deviations. A new joint limit avoidance path-planning method is exerted while maintaining the bounds of upper and lower angles. Also, a new robust motion controller, namely computed-torque-like controller with a variable-structure compensator was applied to the system and compared with computed-torque controller outputs. Thus, showing the efficiency of the mentioned control algorithm in the presence of uncertainties, disturbances, noise, and time delay and its superior performance and robustness in spatial motions are the goals of this paper as well as taking advantage of a new path-planning approach. Firstly, the kinematic formulation of the cables is obtained. Then, a joint limit avoidance theory is used to apply upper and lower bounds for the joint angles. In the next step, Lagrangian dynamic equations for the 3D motions are derived. Subsequently, the positive and unilateral tension conditions in cable-driven systems are applied using null-space solutions. To have precise tracking and robustness with the existence of uncertainties, disturbances, noise, and time delay, a computed-torque control and robust computed-torque-like controller with a variable-structure compensator are utilized for the system. Stability analyses of the controllers are presented and the obtained results are compared for tracking a spatial reference trajectory. Ultimately, this controller witnessed an improvement in the lower limb with the existence of uncertainties and disturbances in terms of the robustness of the given method about 19.5 percent, and in cable forces about 17.1 percent. Improvements for the tracking errors and the control inputs were 10.8 and 7.3 percent in the presence of noise, and 7.3 and 8.6 percent in the presence of the time delay respectively. Similar results were obtained for the upper limb with 21 percent improvement in control inputs and 21.1 percent improvement in tracking performance respectively.