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Robust Sliding Mode Based Finite-time Bilateral Shared Teleoperation System with Unsymmetrical Time-Varying Delay*

This paper presents sliding mode-based finite-time synchronization algorithms for bilateral shared teleoperation systems under unsymmetrical time-varying delay and uncertainty. The synchronization algorithms are designed by using Lyapunov and sliding mode control theory. First, the model-based finite-time synchronization algorithms are designed by using sliding mode control theory with the presence of time-varying delays and uncertainty. Then, robust adaptive finite-time synchronization algorithms are designed for bilateral shared teleoperation systems with the presence of time-varying delays. Adaptive learning algorithms learn and adapt with uncertainty associated with the unmodeled dynamics and external disturbances. Lyapunov analysis shows that the tracking errors between master and slave manipulators converge to the sliding surface in finite time. It also shows that the tracking errors asymptotically converge to zero on the sliding surface. The design provides finite-time convergence of the states to reach the sliding surface as opposed to asymptotic convergence-based bilateral shared teleoperation systems. The design and analysis do not use the exact bound of the uncertainty. In contrast with asymptotic design, finite-time convergence can ensure faster and more robust tracking in the presence of uncertainty and time-varying delays. Unlike reported designs, the proposed algorithms can ensure convergence with the presence of unsymmetrical time-varying delays.