Analysis of Coupled Stability in Multilateral Dual-User Teleoperation Systems

In this paper, we set out a framework for the analysis of coupled stability in dual-user linear teleoperation systems. An extension of the Zeheb-Walach (ZW) criteria for absolute stability of an n-port network will be stated and proven. While the original theorem states conditions for asymptotic stability of a network terminated by passive impedances, the extended version allows for poles on the imaginary axis, which makes it applicable to a larger class of systems, such as robotic applications with position feedback. The extended theorem includes conditions on the Laurent expansion of the elements and the principal minors of the network immittance matrix. A novel dual-user shared control paradigm, realizing a three-way gearbox mechanism, is presented. A numerical analysis of absolute stability of the three-port network, representing the shared control architecture, demonstrates the effectiveness of the extended Zeheb-Walach method.