Multivariable Loop-Shaping in Bilateral Telemanipulation

This paper presents an architecture and control methodology for obtaining transparency and stability robustness in a multivariable bilateral teleoperator system. The work presented here extends a previously published single-input, single-output approach to accommodate multivariable systems. The extension entails the use of impedance control techniques, which are introduced to render linear the otherwise nonlinear dynamics of the master and slave manipulators, in addition to a diagonalization multivariable loop shaping technique, used to render tractable the multivariable compensator design. A multivariable measure of transparency is proposed based on the relative singular values of the environment and transmitted impedance matrices. The approach is experimentally demonstrated on a three degree-of-freedom scaled telemanipulator pair with a highly coupled environment. Using direct measurement of the power delivered to the operator to assess the system’s stability robustness, along with the proposed measure of multivariable transparency, the loop-shaping compensation is shown to improve the stability robustness by a factor of two and the transparency by more than a factor of five.