Adaptive robust control for lower limb rehabilitation robot with uncertainty based on Udwadia–Kalaba approach

Abstract

This paper aims to address the trajectory control of a lower limb rehabilitation robot which works under passive mode. Udwadia–Kalaba approach is a novel and concise method to address the control of constrained systems with holonomic and nonholonomic constraints. According to Udwadia–Kalaba approach, the fundamental equation of lower limb rehabilitation robot considering the resistance of human muscles is first obtained, then a closed-form expression of the joint control torques is obtained. In practice, it is quite difficult to meet the control target due to various uncertainties such as the initial condition deviation from the constraints, the uncertainty of model, and the external disturbance. To deal with this condition, an adaptive control on the basis of Udwadia–Kalaba approach is presented. The uniform boundedness and the uniform ultimate boundedness of the proposed control are verified by the Lyapunov method. Experiments and simulations are performed to show the simplicity, efficiency and accuracy of the proposed control. Specifically, the tracking trajectory of the robot is designed based on the data collected from the experiments. The simulation results show that the proposed control can be used in the lower limb rehabilitation robot.