Iterative learning of impedance control from the viewpoint of passivity

Abstract

This paper proposes an iterative learning control scheme for impedance control of robotic tasks when the tool endpoint covered by soft and deformable material presses a rigid object or environment at a prescribed periodic force pattern. To this end, an iterative learning control scheme for a class of linear dynamical systems with a negative feedback structure is analysed and convergence of the proposed learning update law after a sufficient number of repetitions is proved. It is shown that this convergence realizes impedance matching in a sense of electric circuit theory if the feedback system can be expressed as a lumped‐parameter electric circuit. The iterative learning control scheme is then applied for a case of impedance control of robotic tasks when the characteristics of reproducing force of the deformable material is nonlinear in its displacement and unknown and the tool mass is uncertain. Simulation results are also presented, which show effectiveness of the proposed learning control scheme. Copyright © 2000 John Wiley & Sons, Ltd.

Learnability and Adaptability from the Viewpoint of Passivity Analysis

“…Extensions of this passivity argument for a learning control problem of physical interaction between a finger-tip covered by soft and deformable material and a rigid object arising in robotic tasks have been reported in recent papers [39][40][41] . A further extended discussion of equivalence among learnability, output-dissipativity, and strictly positive realness with an extra condition is found in our next paper 42 .…”

Learnability and Adaptability from the Viewpoint of Passivity Analysis

“…Extensions of this passivity argument for a learning control problem of physical interaction between a finger-tip covered by soft and deformable material and a rigid object arising in robotic tasks have been reported in recent papers [39][40][41] . A further extended discussion of equivalence among learnability, output-dissipativity, and strictly positive realness with an extra condition is found in our next paper 42 .…”

Iterative Learning Control

“…25. In the Wiener filter, for the calculation of G we need to find the inverse of R. But, as shown in (8.63), rank(R) = 1, so the inverse of R does not exist.…”

Iterative learning control for nonsmooth dynamical systems

“…For linear systems Arimoto and Naniwa show in [15] that learnability, invertibility and strictly positive realness are equivalent. For nonlinear systems, Arimoto et al presented in [16] the relation between learnability and strictly output incremental passivity (SOIP), termed as output-dissipativity in [15] and [16].…”

Learnability and Adaptability from the Viewpoint of Passivity Analysis

“…Extensions of this passivity argument for a learning control problem of physical interaction between a finger-tip covered by soft and deformable material and a rigid object arising in robotic tasks have been reported in recent papers [39][40][41] . A further extended discussion of equivalence among learnability, output-dissipativity, and strictly positive realness with an extra condition is found in our next paper 42 .…”

Iterative Learning Control

“…25. In the Wiener filter, for the calculation of G we need to find the inverse of R. But, as shown in (8.63), rank(R) = 1, so the inverse of R does not exist.…”

Iterative learning control for nonsmooth dynamical systems

“…For linear systems Arimoto and Naniwa show in [15] that learnability, invertibility and strictly positive realness are equivalent. For nonlinear systems, Arimoto et al presented in [16] the relation between learnability and strictly output incremental passivity (SOIP), termed as output-dissipativity in [15] and [16].…”

Learnability and Adaptability from the Viewpoint of Passivity Analysis

“…Extensions of this passivity argument for a learning control problem of physical interaction between a finger-tip covered by soft and deformable material and a rigid object arising in robotic tasks have been reported in recent papers [39][40][41] . A further extended discussion of equivalence among learnability, output-dissipativity, and strictly positive realness with an extra condition is found in our next paper 42 .…”

Iterative Learning Control

“…25. In the Wiener filter, for the calculation of G we need to find the inverse of R. But, as shown in (8.63), rank(R) = 1, so the inverse of R does not exist.…”

Iterative learning control for nonsmooth dynamical systems

“…For linear systems Arimoto and Naniwa show in [15] that learnability, invertibility and strictly positive realness are equivalent. For nonlinear systems, Arimoto et al presented in [16] the relation between learnability and strictly output incremental passivity (SOIP), termed as output-dissipativity in [15] and [16].…”