Stability of Nonlinear Time-Delay Systems Describing Human-Robot Interaction

In this paper, we present sufficient conditions for the stability analysis of a stationary point for a special type of nonlinear time-delay systems. These conditions are suitable for analyzing systems describing physical human-robot interaction (pHRI). For this stability analysis a new human model consisting of passive and active elements is introduced and validated. The stability conditions describe parameterization bounds for the human model and an impedance controller. The results of this paper are compared to stability conditions based on passivity, approximated time-delays and to numerical approaches. As a result of the comparison, it is shown that our conditions are more general than the passivity condition of Colgate and Schenkel. This includes the consideration of negative stiffness and nonlinear virtual environments. As an example, a pHRI including a nonlinear virtual environment with a polynomial structure is introduced and also successfully analyzed. These theoretical results could be used in the design of robust controllers and stability observers in pHRI.