Research on Optimization of Nonlinear Extended State Observer for the Upper-Limb Rehabilitation Robot Controller

Abstract

Background: In recent years, patents have shown that upper-limb rehabilitation robots play a significant role in home-based rehabilitation training for stroke hemiplegia patients. Changes in muscle tension during the flaccid paralysis phase cause the rehabilitation robot to deviate from the predetermined motion trajectory. This poses a challenge to the mathematical modeling of the rehabilitation robot and the design of the nonlinear extended state observer (NESO). Objective: To address the problem of trajectory tracking errors caused by the rehabilitation robot when the patient's muscle tension changes, a method based on optimizing the nonlinear function within the NESO is proposed. Methods: First, a mathematical model of the upper-limb rehabilitation robot is established to obtain the dynamic relationship between the robot's velocity and the input voltage. Second, the nonlinear function of NESO is optimized by adjusting the gain values of the sine and tangent functions to effectively estimate the muscle tension and reduce the problem of accumulative error due to changes in muscle tension. Finally, comparative simulations of trajectory tracking including the optimized nonlinear function as well as the sine, tangent and power functions are performed on the MATLAB platform. Results: NESO is constructed to estimate changes in muscle tension based on sine, tangent, and power functions, as well as optimized nonlinear functions. The equivalent gain values of each function and the muscle tension estimation curves of NESO are compared. The simulation results show that the equivalent gain value of the optimized nonlinear function acting in NESO is increased to more than 8 and the convergence time is reduced by 11.9% accordingly. This conclusion is validated by simulations and practical tests. Conclusion: The optimized nonlinear function shortens the estimation time of the NESO for changes in muscle tension, which can provide a reference value for the design of observers for upper-limb rehabilitation robots of patients in the flaccid paralysis stage.