A Comparison Between Lie Group- and Lie Algebra- Based Potential Functions for Geometric Impedance Control

Fuente: arXiv
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Main Authors: Seo, Joohwan, Prakash, Nikhil Potu Surya, Choi, Jongeun, Horowitz, Roberto
Format: Preprint
Published: 2024
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author Seo, Joohwan
Prakash, Nikhil Potu Surya
Choi, Jongeun
Horowitz, Roberto
author_facet Seo, Joohwan
Prakash, Nikhil Potu Surya
Choi, Jongeun
Horowitz, Roberto
contents In this paper, a comparison analysis between geometric impedance controls (GICs) derived from two different potential functions on SE(3) for robotic manipulators is presented. The first potential function is defined on the Lie group, utilizing the Frobenius norm of the configuration error matrix. The second potential function is defined utilizing the Lie algebra, i.e., log-map of the configuration error. Using a differential geometric approach, the detailed derivation of the distance metric and potential function on SE(3) is introduced. The GIC laws are respectively derived from the two potential functions, followed by extensive comparison analyses. In the qualitative analysis, the properties of the error function and control laws are analyzed, while the performances of the controllers are quantitatively compared using numerical simulation.
format Preprint
id arxiv_https___arxiv_org_abs_2401_13190
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle A Comparison Between Lie Group- and Lie Algebra- Based Potential Functions for Geometric Impedance Control
Seo, Joohwan
Prakash, Nikhil Potu Surya
Choi, Jongeun
Horowitz, Roberto
Robotics
Systems and Control
In this paper, a comparison analysis between geometric impedance controls (GICs) derived from two different potential functions on SE(3) for robotic manipulators is presented. The first potential function is defined on the Lie group, utilizing the Frobenius norm of the configuration error matrix. The second potential function is defined utilizing the Lie algebra, i.e., log-map of the configuration error. Using a differential geometric approach, the detailed derivation of the distance metric and potential function on SE(3) is introduced. The GIC laws are respectively derived from the two potential functions, followed by extensive comparison analyses. In the qualitative analysis, the properties of the error function and control laws are analyzed, while the performances of the controllers are quantitatively compared using numerical simulation.
title A Comparison Between Lie Group- and Lie Algebra- Based Potential Functions for Geometric Impedance Control
topic Robotics
Systems and Control
url https://arxiv.org/abs/2401.13190