Lyapunov Based Robust Control for Tracking Control of Lower Limb Rehabilitation Robot with Uncertainty

This study designs a control of two-degree of freedom lower limb rehabilitation robot (LLRR) for the patient who needs the proper physical therapy after a spinal cord injury (SCI), stroke, or a surgical operation. The robot manipulator can perform specified passive exercises as well as copy exercise motions and perform them without the physiotherapist. Specifically, the uncertainties including the model uncertainty, initial condition deviation and the external disturbance are also considered. Firstly, a unilateral man-robot dynamical model is proposed based on Lagrange method. Then, we propose a Lyapunov based robust control to suppress the effect of uncertainties. The control algorithm consists of a PD feedback component and a piecewise function component. Theoretical analysis is provided to demonstrate that the controller can guarantee the uniform boundedness and uniform ultimate boundedness of the system. Moreover, the joint angle trajectory of a healthy person is explicitly obtained by the experimental platform and used as the pre-specified trajectory of the LLRR. Finally, numerical simulation is presented to illustrate the effectiveness and the trajectory-tracking control performance of the control.