Nonlinear optimal control of an active transfemoral prosthesis using state dependent Riccati equation approach

Nowadays, scientific and technological advances have created the ability to replace prosthetic legs with amputated limbs, which the design of a suitable controller is still being discussed by researchers. Therefore, according to the importance of the subject, in this paper, a combination of a nonlinear optimal control method based on the state-dependent Riccati equation approach with the integral state control technique is proposed for an active prosthetic leg for transfemoral amputees. The main objective of this paper is to optimize the energy consumption of the robot/prosthesis system and desirable tracking of the vertical displacement in hip and thigh and knee angles. Also, due to the robustness properties of the suggested controller is investigated sensitivity analysis against ±30% parametric uncertainty and compared with robust adaptive impedance control. The performance of the controller is assessed for both point-to-point motion and tracking modes by considering the saturation bounds of control signals. Finally, the simulation results show a decrease in control effort, desirable performance in tracking, and relatively good robustness in the presence of parametric uncertainty and constant disturbance. Numerical results indicate a significant reduction in energy consumption and total cost in this method compared to the robust adaptive impedance control.