Impedance Control for Robotic Rehabilitation: A Robust Markovian Approach

Abstract

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 system that 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∞ force controller based on the fixed operation mode has also been designed. The Markovian control approach outperformed the H∞ control when all operation modes were taken into account.

Cable-driven lower limb rehabilitation robot

“…In the cases that the proposed structure is not working with value near of load cell mass, the force errors are less than 10%. From the literature, the errors forces found are similar to other prototypes rehabilitation devices [43][44][45][46][47] with errors less than 10% when using PID/trajectory control or impedance control. To compare, the commercial version of InMotion Arm Robot has a force resolution of 0.05 N [48] and a cost of more than USD 100,000 [49].…”

Modeling and Control of a Cable-Driven Rotary Series Elastic Actuator for an Upper Limb Rehabilitation Robot

“…In Wang et al (2019), by designing a sliding surface, a generalized proportional integral observer (GPIO)-based SMC was developed to track the desired trajectory while estimating the time-varying disturbance. A robust regulator for Markovian jump linear systems was proposed for SEA to guarantee the force control robustness in Jutinico et al (2017). In Dos Santos and Siqueira (2014), the desired pole positions for an adaptive controller were determined in consideration of the disturbances on ideal torque source behavior.…”

Stiffness Adjustment for a Single-Link Robot Arm Driven by Series Elastic Actuator in Muscle Training

“…Reference [35] was presented a variable stiffness control, suppressing the vibrations of a single-link robotic arm. An impedance-regulator control approach utilized a Markov chain to transit three modes [36], i.e., fixed, resistive, and passive. An H ∞ gain-scheduled controller was adopted to regulate the stiffness arbitrarily in some interval [37].…”