Teleoperation with memoryless, monotone, and bounded environments: A Zames-Falb multiplier approach

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Absolute stability of bilateral teleoperation has been investigated under the assumption that both human and environment behave as passive systems. This robust design is required since human and environment must be considered as unknown systems at the design stage. If this approach is widely used in the literature, it leads to conservative conditions. Recently, teleoperation has been described in the integral quadratic constraint (IQC) framework, which provides powerful tools to develop less conservative description of both, human and environment. In this initial work, we consider that the environment can be described by a memoryless, monotone, and bounded nonlinearity. Then, Zames-Falb multipliers can be introduced to relax the conservatism of current state-of-the-art stability conditions. The usefulness of our result is shown in a 2-channel position-force teleoperation; where the well known lack of passivity of a PD-F controller is corrected by the use of Zames-Falb multipliers.