Frequency-domain mapping approach of stability bounds for loop shaping of bilateral controllers

Bilateral control architectures include multiple control elements. In general, the relation between a single control element and the stability of the entire system is non-linear. Therefore, stability is standard evaluated a posteriori, rendering the control design process to be complex and highly iterative. A priori understanding of stability constraints would simplify the design of control elements and, as performance is fundamentally limited by stability, could provide specific guidelines whether and how performance of the bilateral teleoperation system can be optimized. This paper presents a numerical visualization method that enables stability-based control design using classical loop-shaping techniques: Frequency-domain Mapping of Bilateral Stability (FMBS). Unlike current stability-based control design approaches, the FMBS method i) is not limited to a fixed control element, a fixed control architecture or system dynamics and ii) enables the implementation of all often used stability criteria. The advantages of the FMBS method are theoretically validated through the use of two test cases, extracted from literature. Using the FMBS method, it is shown that control elements can be redesigned to achieve superior performance.