New stability and tracking criteria for a class of bilateral teleoperation systems

•We propose delay dependent control strategy for a class of bilateral teleoperation system.•New Lyapunov–Krasovskii function uses to show the convergence of the states of the systems.•Stability condition develops in the presence of symmetrical and unsymmetrical delay.•Convergence property derives under passive and constant input forces.•Control design parameters can be calculated a priori.

In this paper, hybrid position and impedance reflection based strategies are presented for bilateral teleoperation systems in the presence of time varying delay. The local and remote platform is coupled by delaying position, position-velocity and impedance reflection characteristics of the input interaction forces between human–master and slave–environment. An adaptation law is used locally to estimate uncertain impedance characteristics of the interaction forces between human and master and between slave and remote environment. The estimated parameter of the impedance characteristics of the interaction force between slave and remote environment are then transmitted with delay back to the master manipulator to adjust the parameter of the target impedance at the human operator hand. Adaptive control terms are also used locally to deal with the uncertainty associated with gravity loading of the master and slave manipulator. By choosing Lyapunov–Krasovskii-like functional, we establish the stability and transparency property of the closed loop teleoperator systems under both symmetrical and unsymmetrical time varying delays. Finally, simulation results are presented to demonstrate the validity of the proposed design for real-time applications.