A Comparison Between Lie Group- and Lie Algebra- Based Potential Functions for Geometric Impedance Control
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914650791084032 |
|---|---|
| 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 |