Complementary Stability of Markovian Systems: Series Elastic Actuators and Human-Robot Interaction

Abstract

This paper presents an extension of the complementary stability analysis for discrete-time Markovian systems applied in interaction control. The control strategy considers an internal loop force control for Series Elastic Actuators based on the Robust Regulator for Discrete-time Markov Jump Linear systems and extern loop impedance control to regulate the interaction between the human and robot. Two examples show the complementary stability analysis of the human-robot interaction system, where is regarded as different values of the virtual impedances, different levels for the robustness of the force control, uncertainties, and abrupt changes for human parameters. Simulation results show the capacity of control strategy to deal with active interaction models, where the Mean Square Stability guarantees safe for the user. Additionally, from results it is understood the transmissibility of impedance achieved is a consequence of the robust performance given by the force controller.