Stable Robust Adaptive Impedance Control of a Prosthetic Leg

Abstract

We propose a nonlinear robust model reference adaptive impedance controller for an active prosthetic leg for transfemoral amputees. We use an adaptive control term to consider the uncertain parameters of the system, and a robust control term so the system trajectories converge to a sliding mode boundary layer and exhibit robustness to variations of ground reaction force (GRF). The boundary layer not only compromises between control chattering and tracking performance, but also bounds the parameter adaptation to prevent unfavorable parameter drift. We also prove the stability of the controller for the robotic system in the case of non-scalar boundary layer trajectories using Lyapunov stability theory and Barbalat’s lemma. The acceleration-free regressor form of the system removes the need to measure the joint accelerations, which would otherwise introduce noise in the system. We use particle swarm optimization (PSO) to optimize the design parameters of the controller and the adaptation law. The PSO cost function is comprised of control signal magnitudes and tracking errors. PSO achieves a 8% improvement in the objective function. Finally, we present simulation results to validate the effectiveness of the controller. We achieve good tracking of joint displacements and velocities for both nominal and perturbed values of the system parameters. Variations of ±30% on the system parameters result in an increase of the cost function by only 3%, which confirms the robustness of the controller.