Exponential Set-Point Stabilization of Underactuated Vehicles Moving in Three-Dimensional Space
(2022) In IEEE/CAA Journal of Automatica Sinica 9(2). p.270-282- Abstract
This paper investigates the stabilization of underactuated vehicles moving in a three-dimensional vector space. The vehicle's model is established on the matrix Lie group SE(3), which describes the configuration of rigid bodies globally and uniquely. We focus on the kinematic model of the underactuated vehicle, which features an underactuation form that has no sway and heave velocity. To compensate for the lack of these two velocities, we construct additional rotation matrices to generate a motion of rotation coupled with translation. Then, the state feedback is designed with the help of the logarithmic map, and we prove that the proposed control law can exponentially stabilize the underactuated vehicle to the identity group element... (More)
This paper investigates the stabilization of underactuated vehicles moving in a three-dimensional vector space. The vehicle's model is established on the matrix Lie group SE(3), which describes the configuration of rigid bodies globally and uniquely. We focus on the kinematic model of the underactuated vehicle, which features an underactuation form that has no sway and heave velocity. To compensate for the lack of these two velocities, we construct additional rotation matrices to generate a motion of rotation coupled with translation. Then, the state feedback is designed with the help of the logarithmic map, and we prove that the proposed control law can exponentially stabilize the underactuated vehicle to the identity group element with an almost global domain of attraction. Later, the presented control strategy is extended to set-point stabilization in the sense that the underactuated vehicle can be stabilized to an arbitrary desired configuration specified in advance. Finally, simulation examples are provided to verify the effectiveness of the stabilization controller.
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- author
- He, Xiaodong ; Sun, Zhiyong LU ; Geng, Zhiyong and Robertsson, Anders LU
- organization
- publishing date
- 2022-02-01
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Exponential stabilization, logarithmic feedback, matrix Lie group, underactuated vehicle
- in
- IEEE/CAA Journal of Automatica Sinica
- volume
- 9
- issue
- 2
- pages
- 13 pages
- publisher
- IEEE - Institute of Electrical and Electronics Engineers Inc.
- external identifiers
-
- scopus:85118936573
- ISSN
- 2329-9266
- DOI
- 10.1109/JAS.2021.1004323
- language
- English
- LU publication?
- yes
- additional info
- Publisher Copyright: © 2014 Chinese Association of Automation.
- id
- 6dc3cd69-c94b-46e4-9609-5571aecd8615
- date added to LUP
- 2021-12-02 12:29:55
- date last changed
- 2023-05-11 08:02:57
@article{6dc3cd69-c94b-46e4-9609-5571aecd8615,
abstract = {{<p>This paper investigates the stabilization of underactuated vehicles moving in a three-dimensional vector space. The vehicle's model is established on the matrix Lie group SE(3), which describes the configuration of rigid bodies globally and uniquely. We focus on the kinematic model of the underactuated vehicle, which features an underactuation form that has no sway and heave velocity. To compensate for the lack of these two velocities, we construct additional rotation matrices to generate a motion of rotation coupled with translation. Then, the state feedback is designed with the help of the logarithmic map, and we prove that the proposed control law can exponentially stabilize the underactuated vehicle to the identity group element with an almost global domain of attraction. Later, the presented control strategy is extended to set-point stabilization in the sense that the underactuated vehicle can be stabilized to an arbitrary desired configuration specified in advance. Finally, simulation examples are provided to verify the effectiveness of the stabilization controller. </p>}},
author = {{He, Xiaodong and Sun, Zhiyong and Geng, Zhiyong and Robertsson, Anders}},
issn = {{2329-9266}},
keywords = {{Exponential stabilization; logarithmic feedback; matrix Lie group; underactuated vehicle}},
language = {{eng}},
month = {{02}},
number = {{2}},
pages = {{270--282}},
publisher = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
series = {{IEEE/CAA Journal of Automatica Sinica}},
title = {{Exponential Set-Point Stabilization of Underactuated Vehicles Moving in Three-Dimensional Space}},
url = {{http://dx.doi.org/10.1109/JAS.2021.1004323}},
doi = {{10.1109/JAS.2021.1004323}},
volume = {{9}},
year = {{2022}},
}