TOWARDS ROBUST BILATERAL TELEOPERATION WITH NONLINEAR ENVIRONMENTS VIA MULTIPLIER APPROACH

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Abstract

This thesis provides moderate stability conditions for bilateral teleoperation by exploiting the advantages of the Zames-Falb multipliers within the integral quadratic constraint 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. Because the classes of multipliers have infinite dimension, parametrization of these multipliers is used to obtain convex searches over a finite number of parameters such that an asymmetric Zames-Falb multiplier search is proposed. The stability of the system is analysed as a Lur̢۪e system containing time-delay and monotone bounded nonlinearity. As a result, (less) conservative (than typical) delay-dependent stability conditions can be developed. Performance of the results is initially evaluated with case studies based on the numerical examples from the neural networks while using Kalman conjecture as a benchmark. Also, a geometrically intuitive stability analysis approach is provided to show when the Kalman conjecture is true for the time delayed Lur̢۪e interconnections. Thus, one can show that it is possible to find a multiplier for a slope bound equivalent to the Nyquist value without constructing the suitable multiplier by revisiting classical results in clockwise properties of the plants with time delay. Then, these results are applied to the bilateral teleoperation. Finally, stability conditions are tested with different control architectures and experimentations; in particular, bilateral teleoperation experiments over the internet between Manchester, UK, and Vigo, Spain, are carried out. The advantage of the proposed approach is demonstrated by reaching higher transparency indices for a two-channel positionforce and for three-channel bilateral teleoperation architectures while ensuring the absolute stability with nonlinear environments.

Keyword(s)

Absolute stability ; Bilateral Teleoperation

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