Model-free robust adaptive integral sliding mode impedance control of knee-ankle-toe active transfemoral prosthesis.

Background: Wearing appropriate active prosthesis is the guarantee of daily life for amputees. Normally the controller of the traditional active transfemoral prosthesis is designed based on the mathematical model. The modelling error and the external interference will reduce the control accuracy of the system and make the prosthesis unable to operate in the desired trajectory.

Methods: Firstly, combined with time delay estimation (TDE), a model-free robust integral sliding mode impedance controller is designed. This method not only suppress the impedance error, but also eliminate the nonlinear relationship and disturbance in the dynamic model. Secondly, an adaptive law is proposed to update the controller gain, which provide stable control effect. Thirdly, the stability of prosthesis closed-loop system is proved by Lyapunov stability theory. Finally, the motor torque is used to drive each joint, and Matlab/Simscape is used to verify the prosthesis control system.

Results: From the result of the simulation experiment, the control method has a good tracking effect on each joint. The root mean square error and mean absolute errors of each joint's angle tracking error are 0.6123°, 1.9976°, 0.5574° and 0.2635°, 1.8175°, 0.4796°. Compared with the controller without adaptive gain and impedance control, the control effect is improved, and the plantar pressure of amputees is closer to the sound side.

Conclusions: Comparing the results of different controllers, the adaptive integral sliding mode impedance controller with TDE can better track the expected angles of each joint. The gait is more normal. The walking performance of the prosthesis wearers is improved.