A nonlinear robust optimal controller for an active transfemoral prosthesis: An estimator-based state-dependent Riccati equation approach

This article presents an estimator-based nonlinear robust optimal controller for an active prosthetic leg for transfemoral amputees. The proposed controller is derived from a combination of the state-dependent Riccati equation technique to optimize the energy consumption of the robot/prosthesis system and the sliding mode control to reduce the effects of the model parametric uncertainties and ground reaction forces as nonparametric uncertainties. In addition, the integral state control technique is employed to improve tracking; also, to have a compromise between tracking performance and control signal chattering, the boundary layer is then used. In this study, the performance of both the controller and estimator in the presence of noise and disturbance is assessed for nominal system while ±40% parametric uncertainty with respect to saturation bounds of control signals is considered. The results of the simulation in this research with ±40% parametric uncertainty compared to a robust adaptive impedance control approach with the only variation of ±30% on the system parameters, show high performance of the proposed controllers in reducing energy consumption, good robustness, improved position tracking performance, and good performance in estimating state variables, even in the presence of large initial errors compared to the extended Kalman filter.