Adaptive schemes for stable teleoperation with communication delay based on IOS small gain theorem

The problem of adaptive stabilization of the force-reflecting telerobotic system in presence of time delay in the communication channel is addressed. We propose two adaptive control schemes that make the overall telerobotic system input-to-state stable (ISS) with respect to external forces for any constant communication delay. In particular, in case where the joint velocity measurements are replaced by the estimates obtained using "dirty derivative" filters, we show the input-to-state stability in the semiglobal practical sense. These results are based on a new version of the IOS (input-to-output stability) small gain theorem for functional differential equations.