Impedance Control for Robotic Rehabilitation: A Robust Markovian Approach

The human-robot interaction has played an important role in rehabilitation robotics and impedance control has been used in the regulation of interaction forces between the robot actuator and human limbs. Series elastic actuators (SEAs) have been an efficient solution in the design of this kind of robotic application. Standard implementations of impedance control with SEAs require an internal force control loop for guaranteeing the desired impedance output. However, nonlinearities and uncertainties hamper such a guarantee of an accurate force level in this human-robot interaction. This paper addresses the dependence of the impedance control performance on the force control and proposes a control approach that improves the force control robustness. A unified model of the human-robot systemthat considers the ankle impedance by a second-order dynamics subject to uncertainties in the stiffness, damping, and inertia parameters has been developed. Fixed, resistive, and passive operation modes of the robotics system were defined, where transition probabilities among the modes were modeled through a Markov chain. A robust regulator for Markovian jump linear systems was used in the design of the force control. Experimental results show the approach improves the impedance control performance. For comparison purposes, a standard H-infinity force controller based on the fixed operation mode has also been designed. The Markovian control approach outperformed the H-infinity control when all operation modes were taken into account.