Joint Space Stiffness and Damping for Cartesian and Null Space Impedance Control of Redundant Robotic Manipulators

Carlos Saldarriaga; Nilanjan Chakraborty; Imin Kao

doi:10.1007/978-3-030-95459-8_25

Joint Space Stiffness and Damping for Cartesian and Null Space Impedance Control of Redundant Robotic Manipulators

Carlos Saldarriaga
, Nilanjan Chakraborty
, Imin Kao

Mechanical Engineering

Stony Brook University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

7 Scopus citations

Abstract

Cartesian impedance control has been widely used in controlling robotic manipulators for manipulation and assembly tasks to compute the required joint torques and/or end-effector forces. Current congruence mapping of the Cartesian stiffness and damping matrices to joint spaces are not valid for general cases. In this paper, we derive from first principles, the general form of the mapping of the stiffness and damping matrices between Cartesian and joint space, which applies to all general cases. The new results show the coupling of Cartesian damping in the stiffness after mapping to the joint space, which is not found in the literature. By applying principle of vibration analysis and including the null space tasks, we can choose the stiffness and damping matrices in order to achieve prescribed dynamic response. Such analysis also enables us to gain a deeper understanding of the responses versus the parameters of robot manipulators; for example, certain elements only affect dynamic responses in specific directions.

Original language	English
Title of host publication	Robotics Research - The 19th International Symposium ISRR
Editors	Tamim Asfour, Eiichi Yoshida, Jaeheung Park, Henrik Christensen, Oussama Khatib
Publisher	Springer Nature
Pages	410-426
Number of pages	17
ISBN (Print)	9783030954581
DOIs	https://doi.org/10.1007/978-3-030-95459-8_25
State	Published - 2022
Event	17th International Symposium of Robotics Research, ISRR 2019 - Hanoi, Viet Nam Duration: Oct 6 2019 → Oct 10 2019

Publication series

Name	Springer Proceedings in Advanced Robotics
Volume	20 SPAR
ISSN (Print)	2511-1256
ISSN (Electronic)	2511-1264

Conference

Conference	17th International Symposium of Robotics Research, ISRR 2019
Country/Territory	Viet Nam
City	Hanoi
Period	10/6/19 → 10/10/19

Keywords

Control
Damping
Impedance
Joint space
Manipulation
Null space
Stiffness
Task space

Access to Document

10.1007/978-3-030-95459-8_25

Cite this

Saldarriaga, C., Chakraborty, N., & Kao, I. (2022). Joint Space Stiffness and Damping for Cartesian and Null Space Impedance Control of Redundant Robotic Manipulators. In T. Asfour, E. Yoshida, J. Park, H. Christensen, & O. Khatib (Eds.), Robotics Research - The 19th International Symposium ISRR (pp. 410-426). (Springer Proceedings in Advanced Robotics; Vol. 20 SPAR). Springer Nature. https://doi.org/10.1007/978-3-030-95459-8_25

Saldarriaga, Carlos ; Chakraborty, Nilanjan ; Kao, Imin. / Joint Space Stiffness and Damping for Cartesian and Null Space Impedance Control of Redundant Robotic Manipulators. Robotics Research - The 19th International Symposium ISRR. editor / Tamim Asfour ; Eiichi Yoshida ; Jaeheung Park ; Henrik Christensen ; Oussama Khatib. Springer Nature, 2022. pp. 410-426 (Springer Proceedings in Advanced Robotics).

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title = "Joint Space Stiffness and Damping for Cartesian and Null Space Impedance Control of Redundant Robotic Manipulators",

abstract = "Cartesian impedance control has been widely used in controlling robotic manipulators for manipulation and assembly tasks to compute the required joint torques and/or end-effector forces. Current congruence mapping of the Cartesian stiffness and damping matrices to joint spaces are not valid for general cases. In this paper, we derive from first principles, the general form of the mapping of the stiffness and damping matrices between Cartesian and joint space, which applies to all general cases. The new results show the coupling of Cartesian damping in the stiffness after mapping to the joint space, which is not found in the literature. By applying principle of vibration analysis and including the null space tasks, we can choose the stiffness and damping matrices in order to achieve prescribed dynamic response. Such analysis also enables us to gain a deeper understanding of the responses versus the parameters of robot manipulators; for example, certain elements only affect dynamic responses in specific directions.",

keywords = "Control, Damping, Impedance, Joint space, Manipulation, Null space, Stiffness, Task space",

author = "Carlos Saldarriaga and Nilanjan Chakraborty and Imin Kao",

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Saldarriaga, C, Chakraborty, N & Kao, I 2022, Joint Space Stiffness and Damping for Cartesian and Null Space Impedance Control of Redundant Robotic Manipulators. in T Asfour, E Yoshida, J Park, H Christensen & O Khatib (eds), Robotics Research - The 19th International Symposium ISRR. Springer Proceedings in Advanced Robotics, vol. 20 SPAR, Springer Nature, pp. 410-426, 17th International Symposium of Robotics Research, ISRR 2019, Hanoi, Viet Nam, 10/6/19. https://doi.org/10.1007/978-3-030-95459-8_25

Joint Space Stiffness and Damping for Cartesian and Null Space Impedance Control of Redundant Robotic Manipulators. / Saldarriaga, Carlos; Chakraborty, Nilanjan ; Kao, Imin.
Robotics Research - The 19th International Symposium ISRR. ed. / Tamim Asfour; Eiichi Yoshida; Jaeheung Park; Henrik Christensen; Oussama Khatib. Springer Nature, 2022. p. 410-426 (Springer Proceedings in Advanced Robotics; Vol. 20 SPAR).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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T1 - Joint Space Stiffness and Damping for Cartesian and Null Space Impedance Control of Redundant Robotic Manipulators

AU - Saldarriaga, Carlos

AU - Chakraborty, Nilanjan

AU - Kao, Imin

PY - 2022

Y1 - 2022

N2 - Cartesian impedance control has been widely used in controlling robotic manipulators for manipulation and assembly tasks to compute the required joint torques and/or end-effector forces. Current congruence mapping of the Cartesian stiffness and damping matrices to joint spaces are not valid for general cases. In this paper, we derive from first principles, the general form of the mapping of the stiffness and damping matrices between Cartesian and joint space, which applies to all general cases. The new results show the coupling of Cartesian damping in the stiffness after mapping to the joint space, which is not found in the literature. By applying principle of vibration analysis and including the null space tasks, we can choose the stiffness and damping matrices in order to achieve prescribed dynamic response. Such analysis also enables us to gain a deeper understanding of the responses versus the parameters of robot manipulators; for example, certain elements only affect dynamic responses in specific directions.

AB - Cartesian impedance control has been widely used in controlling robotic manipulators for manipulation and assembly tasks to compute the required joint torques and/or end-effector forces. Current congruence mapping of the Cartesian stiffness and damping matrices to joint spaces are not valid for general cases. In this paper, we derive from first principles, the general form of the mapping of the stiffness and damping matrices between Cartesian and joint space, which applies to all general cases. The new results show the coupling of Cartesian damping in the stiffness after mapping to the joint space, which is not found in the literature. By applying principle of vibration analysis and including the null space tasks, we can choose the stiffness and damping matrices in order to achieve prescribed dynamic response. Such analysis also enables us to gain a deeper understanding of the responses versus the parameters of robot manipulators; for example, certain elements only affect dynamic responses in specific directions.

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Saldarriaga C, Chakraborty N , Kao I. Joint Space Stiffness and Damping for Cartesian and Null Space Impedance Control of Redundant Robotic Manipulators. In Asfour T, Yoshida E, Park J, Christensen H, Khatib O, editors, Robotics Research - The 19th International Symposium ISRR. Springer Nature. 2022. p. 410-426. (Springer Proceedings in Advanced Robotics). doi: 10.1007/978-3-030-95459-8_25