L 1 impedance control for bilateral teleoperation containing model uncertainty

Restricting transient peaks of contact force in teleoperation systems is undeniably vital, specially in critical applications such as telesurgery. This issue, however, has still remained unsolved in the literature. In order to address this problem, we propose an impedance control scheme using optimal L₁ theory for teleoperation systems encompassing asymmetric randomly time-varying delays and model uncertainties. To this end, an L₁-based state-feedback compensator is designed employing linear matrix inequalities, aiming at minimizing the desired impedance error subjected to human force as exogenous disturbance. A simulation is ultimately conducted in comparison with the sliding-mode-based impedance controller. The results validate that the proposed controller is able to keep the integral of impedance error within the desired bound and, thus, improves the transient response. This is, however, at the expense of imposing a steady-state error for the integral of impedance error, which is normally made zero by the sliding-mode controller.