Generalization of Impedance Matching to Nonlinear Dynamics of Robot Tasks

Abstract

This paper aims at generalizing the concept of impedance matching to nonlinear circuits that express nonlinear dynamics of robot tasks, where a tool endpoint (or fingertip) with soft material presses a rigid and fixed object or environment. Under such a situation that characteristics of reproducing force of the elastic material with respect to displacement is nonlinear and unknown, impedance control is established by constructing a negative feedback connection of two hyperstable blocks. Then, the minimum upper-bound of the average power of force error under the existence of measurement noises of both displacement and force is derived in a sense of H-infinity disturbance attenuation, which corresponds to a generalization of the well-known theorem of maximum power transfer for impedance matching of linear electric circuits. Choice of design parameters is discussed from the viewpoint of better matching of two passive blocks to attain optimal transient response and attenuation of the effect of disturbances.