On the stiffness control and congruence transformation using the conservative congruence transformation (CCT)

Y. Li; I. Kao

On the stiffness control and congruence transformation using the conservative congruence transformation (CCT)

Y. Li
, I. Kao

Mechanical Engineering

Stony Brook University

Research output: Contribution to journal › Conference article › peer-review

7 Scopus citations

Abstract

The conservative congruence transformation (CCT), K_θ - K_g = J_θ^TK_pJ_θ, was proposed by Chen and Kao as the correct congruence transformation to replace the conventional mapping, K_θ = J_θ^TK_pJ_θ, proposed by Salisbury in 1980. The conventional mapping was shown to lead to physically inconsistent results when external force is present in stiffness control. Theoretical proofs are also provided to show the conservative nature of the CCT, and the non-conservative property of the conventional mapping. The CCT is established as the general and valid mapping of the stiffness matrices between the joint and Cartesian spaces of robotic manipulators. In this paper, the work of CCT is extended to a redundant planar manipulator. Numerical simulations are presented to illustrate issues related to the application of generalized inverse in the analysis of redundant manipu lators.

Original language	English
Pages (from-to)	3937-3942
Number of pages	6
Journal	Proceedings - IEEE International Conference on Robotics and Automation
Volume	4
State	Published - 2001
Event	2001 IEEE International Conference on Robotics and Automation (ICRA) - Seoul, Korea, Republic of Duration: May 21 2001 → May 26 2001

Cite this

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title = "On the stiffness control and congruence transformation using the conservative congruence transformation (CCT)",

abstract = "The conservative congruence transformation (CCT), Kθ - Kg = JθTKpJθ, was proposed by Chen and Kao as the correct congruence transformation to replace the conventional mapping, Kθ = JθTKpJθ, proposed by Salisbury in 1980. The conventional mapping was shown to lead to physically inconsistent results when external force is present in stiffness control. Theoretical proofs are also provided to show the conservative nature of the CCT, and the non-conservative property of the conventional mapping. The CCT is established as the general and valid mapping of the stiffness matrices between the joint and Cartesian spaces of robotic manipulators. In this paper, the work of CCT is extended to a redundant planar manipulator. Numerical simulations are presented to illustrate issues related to the application of generalized inverse in the analysis of redundant manipu lators.",

author = "Y. Li and I. Kao",

year = "2001",

language = "English",

volume = "4",

pages = "3937--3942",

journal = "Proceedings - IEEE International Conference on Robotics and Automation",

issn = "1050-4729",

note = "2001 IEEE International Conference on Robotics and Automation (ICRA) ; Conference date: 21-05-2001 Through 26-05-2001",

}

TY - JOUR

T1 - On the stiffness control and congruence transformation using the conservative congruence transformation (CCT)

AU - Li, Y.

AU - Kao, I.

PY - 2001

Y1 - 2001

N2 - The conservative congruence transformation (CCT), Kθ - Kg = JθTKpJθ, was proposed by Chen and Kao as the correct congruence transformation to replace the conventional mapping, Kθ = JθTKpJθ, proposed by Salisbury in 1980. The conventional mapping was shown to lead to physically inconsistent results when external force is present in stiffness control. Theoretical proofs are also provided to show the conservative nature of the CCT, and the non-conservative property of the conventional mapping. The CCT is established as the general and valid mapping of the stiffness matrices between the joint and Cartesian spaces of robotic manipulators. In this paper, the work of CCT is extended to a redundant planar manipulator. Numerical simulations are presented to illustrate issues related to the application of generalized inverse in the analysis of redundant manipu lators.

AB - The conservative congruence transformation (CCT), Kθ - Kg = JθTKpJθ, was proposed by Chen and Kao as the correct congruence transformation to replace the conventional mapping, Kθ = JθTKpJθ, proposed by Salisbury in 1980. The conventional mapping was shown to lead to physically inconsistent results when external force is present in stiffness control. Theoretical proofs are also provided to show the conservative nature of the CCT, and the non-conservative property of the conventional mapping. The CCT is established as the general and valid mapping of the stiffness matrices between the joint and Cartesian spaces of robotic manipulators. In this paper, the work of CCT is extended to a redundant planar manipulator. Numerical simulations are presented to illustrate issues related to the application of generalized inverse in the analysis of redundant manipu lators.

UR - https://www.scopus.com/pages/publications/0034860486

M3 - Conference article

AN - SCOPUS:0034860486

SN - 1050-4729

VL - 4

SP - 3937

EP - 3942

JO - Proceedings - IEEE International Conference on Robotics and Automation

JF - Proceedings - IEEE International Conference on Robotics and Automation

T2 - 2001 IEEE International Conference on Robotics and Automation (ICRA)

Y2 - 21 May 2001 through 26 May 2001

ER -

On the stiffness control and congruence transformation using the conservative congruence transformation (CCT)

Abstract

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