Variable impedance control has been required to perform a variety of interactive tasks in contact with environments. In some cases, the time-varying stiffness matrix of the impedance model can be used to achieve high performance for uneven contact tasks. In the paper, two sufficient conditions are proposed to ensure the input-to-state stability (ISS) irrespective of time-varying stiffness. Furthermore, the update rule of the stiffness is also suggested in such a way that the asymptotic stability is guaranteed under certain region conditions. Even when the update rule is not applied, the ISS is at least assured. In other words, the error is always bounded only if the external force/torque is bounded. In detail, two sufficient conditions offer the lower bound of stiffness and the upper bound of its time derivative. Simulation results show that the ISS of variable impedance control is achieved if the proposed sufficient conditions are satisfied. Also, we can confirm the asymptotic behavior in the simulation when the stiffness is updated according to the given rule.
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