  Robots are used by humans not only as tools but also to interactively assist
and cooperate with humans, thereby forming physical human-robot interactions.
In these interactions, there is a risk that a feedback loop causes unstable
force interaction, in which force escalation exposes a human to danger.
Previous studies have analyzed the stability of voluntary interaction but have
neglected involuntary behavior in the interaction. In contrast to the previous
studies, this study considered the involuntary behavior: a human's force
reproduction bias for discrete-event human-robot force interaction. We derived
an asymptotic stability condition based on a mathematical bias model and found
that the bias asymptotically stabilizes a human's implicit equilibrium point
far from the implicit equilibrium point and destabilizes the point near the
point. The bias model, convergence of the interaction toward the implicit
equilibrium point, and divergence around the point were consistently verified
via behavioral experiments under three kinds of interactions using three
different body parts: a hand finger, wrist, and foot. Our results imply that
humans implicitly secure a stable and close relationship between themselves and
robots with their involuntary behavior.
