Stabilization of bilateral teleoperators with asymmetric stochastic delay

In this paper we consider the problem of position tracking and error boundedness for a master–slave teleoperation system when the communication channel is characterized by a time-varying stochastic delay. In particular, we assume the delay to be a time-varying Markov regime switching process. Our solution is based on a suitable proportional–derivative (PD) like controller. Exploiting a Lyapunov–Krasovskii functional approach, we are able to show that the velocity and position errors remain bounded, provided specific inequality is satisfied. Moreover, zero steady-state position error is achieved when the human operator and the environment do not interact with the system. In order to be able to exploit Lyapunov–Krasovskii approach we need to lift the underlying process to an infinite-dimensional process taking values in a suitable Banach space so that, in the new space, the process is a Markov process. Our conditions for guaranteeing boundedness and the zero steady-state position tracking error are the natural generalization of the deterministic counterparts available in the literature, i.e. when considering the trivial case of a single-state Markov process previous results are recovered. Simulation results show the effectiveness of the proposed approach.