Stability Analysis of Bilateral Teleoperation with Bounded and Monotone Environments via Zames-Falb Multipliers

This paper provides less conservative stability conditions for bilateral teleoperation by exploiting the advantages of the integral quadratic constraint (IQC) framework, where the environment can be defined as a memoryless, bounded, and monotonic nonlinear operator. Recent advances in multiplier theory for appropriate classes of uncertainties/nonlinearities are applied. Since the classes of multipliers have infinite dimension, parametrization of these multipliers is used to obtain convex searches over a finite number of parameters. The stability of the system is analysed as a Lurye system containing timedelay and monotone nonlinearity. As a result, less conservative delay-dependent conditions can be developed. These results are then applied to bilateral teleoperation. Finally, stability results are tested with different experiments; in particular bilateral teleoperation experiments over the internet between Manchester, UK, and Vigo, Spain, have been carried out. The advantage of the proposed approach is demonstrated by reaching higher transparency index for 2-channel position-force teleoperation while ensuring absolute stability.