Position synchronization for an uncertain teleoperation system with time delays using L1 theory

The problem of position tracking in teleoperation systems containing latencies and dynamical uncertainties is addressed in this work. In many applications, such as telesurgery, safe interaction with the external environment is a factor which may undermine the synchronization of the positions. For nondestructive contact with the environment, in addition to an errorless steady-state position tracking, the closed-loop system requires to have a response with the least possible overshoot. To this end, a state-feedback controller based upon L1 theory is proposed in this work. The compensator is synthesized utilizing the linear matrix inequality (LMI) technology, and the asymptotic stability of the system is verified employing Lyapunov-Krasovskii functional. Another advantage of the proposed control scheme is that it is robust to asymmetric randomly varying time delays in the communication channels. The L1-based controller is finally compared to the well-known sliding mode controller via simulation, and is proved to outperform it from maximum error point of view, while preserving low steady-state error. The proposed controller is also illustrated to be effective even in the presence of model uncertainties.