Robust adaptive impedance control with application to a transfemoral prosthesis and test robot

This paper presents, compares, and tests two robust model reference adaptive impedance controllers for a three degrees-of-freedom (3DOF) powered prosthesis/test robot. We first present a model for a combined system that includes a test robot and a transfemoral prosthetic leg. We design these two controllers, so the error trajectories of the system converge to a boundary layer and the controllers show robustness to ground reaction forces (GRFs) as nonparametric uncertainties and also handle model parameter uncertainties. We prove the stability of the closed-loop systems for both controllers for the prosthesis/ test robot in the case of nonscalar boundary layer trajectories using Lyapunov stability theory and Barbalat's lemma. We design the controllers to imitate the biomechanical properties of able-bodied walking and to provide smooth gait. We finally present simulation results to confirm the efficacy of the controllers for both nominal and off-nominal system model parameters. We achieve good tracking of joint displacements and velocities, and reasonable control and GRF magnitudes for both controllers. We also compare performance of the controllers in terms of tracking, control effort, and parameter estimation for both nominal and off-nominal model parameters.