Stability analysis for a passive/active human model in physical human–robot interaction with multiple users

ABSTRACT

Human–robot–human interaction (HRH), understood as a physical human–robot interaction (pHRI) with two humans, can be applied when lifting heavy, bulky and large-sized objects with a robot. In combination with a virtual environment, this system can become nonlinear. In this article, we prove sufficient stability conditions for a stationary point of such a particular type of nonlinear multiple time-delay systems. In addition, a new human model consisting of a passive and an active part will be introduced and validated on experimental data. The derived stability conditions are applied to a single-user pHRI system including this human model. The results indicate that these conditions are very conservative. Then four approaches for the analysis of a multi-user pHRI are introduced and compared with each other. Finally, a potential HRH application with a nonlinear environment in the form of a potential force field is presented.

KEYWORDS:

• Physical human–robot interaction
• nonlinear time-delay systems
• Lyapunov–Krasovskii functional
• human–robot–human
• impedance control

ORCID

Florian Müller http://orcid.org/0000-0002-4339-7875

Notes

1 If n is odd, $z=(x_1{x_2}^n{)}^T$.

2 If n is odd, it is possible to use the ordinary derivative.