Extension of Zeheb-Walach absolute stability criteria for robot-human interactions

The notion of absolute stability has been used to analyze the stability of man-machine interfaces in which a human operator commands a robot to do a task in a real or simulated environment. In this paper, we present and prove an extended version of the Zeheb-Walach absolute stability theorem that can be applied to n-port networks with “simple imaginary poles”. Conditions on the Laurent expansion of the elements and the principal minors of the impedance matrix are added to the theorem and the proof is conducted using the zero set of multiparameter functions. The unique feature of the proposed method is the graphical representation of the loci of the roots of the system, which allows for studying the effect of various system and control parameters on stability margins. To demonstrate the applicability of the new theorem, the stability of a position-position controlled teleoperation system, modeled by a 2-port network, coupled with the passive impedances of the human operator's hand, and the environment, is investigated.