Exponential Set-Point Stabilization of Underactuated Vehicles Moving in Three-Dimensional Space

Xiaodong He; Zhiyong Sun; Zhiyong Geng; Anders Robertsson

doi:10.1109/JAS.2021.1004323

Volume 9 Issue 2

Feb. 2022

IEEE/CAA Journal of Automatica Sinica

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2022 > 9(2): 270-282

X. D. He, Z. Y. Sun, Z. Y. Geng, and A. Robertsson, “Exponential set-point stabilization of underactuated vehicles moving in three-dimensional space,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 2, pp. 270–282, Feb. 2022. doi: 10.1109/JAS.2021.1004323

Citation:

X. D. He, Z. Y. Sun, Z. Y. Geng, and A. Robertsson, “Exponential set-point stabilization of underactuated vehicles moving in three-dimensional space,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 2, pp. 270–282, Feb. 2022. doi: 10.1109/JAS.2021.1004323

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Exponential Set-Point Stabilization of Underactuated Vehicles Moving in Three-Dimensional Space

doi: 10.1109/JAS.2021.1004323

1.
State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing 100871, China
2.
Department of Electrical Engineering, Eindhoven University of Technology (TU/e), 5600 MB Eindhoven, the Netherlands
3.
Department of Automatic Control, LTH, Lund University, 22100 Lund, Sweden

Funds: This work was supported by the National Natural Science Foundation of China (61773024, 62073002), the Eindhoven Artificial Intelligence Systems Institute (EAISI), and the ELLIIT Excellence Center and the Swedish Foundation for Strategic Research, Sweden (RIT15-0038)

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Author Bio:
Xiaodong He received the B.Eng. degree from China University of Petroleum, in 2016, and the Ph.D. degree from Peking University, in 2021. He is currently a Postdoctoral Research Fellow with the College of Engineering, Peking University. His research interests include cooperative control of nonholonomic vehicles and geometric control of underactuated mechanical systems

Zhiyong Sun (Member, IEEE) received the Ph.D. degree from Australian National University (ANU), Canberra ACT, Australia, in February 2017. He was a Research Fellow/Lecturer with the Research School of Engineering, ANU, from 2017 to 2018. From June 2018 to January 2020, he worked as a Postdoctoral Researcher at the Department of Automatic Control, Lund University, Lund, Sweden. Since January 2020 he has joined Eindhoven University of Technology (TU/e), the Netherlands, as an Assistant Professor. His research interests include multi-agent systems, control of autonomous formations, and distributed optimization

Zhiyong Geng received the B.Sc. and M.Sc. degrees from Northeast University, in 1981 and 1984, respectively, and the Ph.D. degree from the Academy of Mathematics and Systems Science, Chinese Academy of Sciences, in 1995. From 1995 to 1997, he served as a Postdoctoral Research Fellow with the Department of Mechanics and Engineering Science, Peking University, where he is currently a Full Professor. His research interests include nonlinear control, robust control, and geometric control of mechanical systems

Anders Robertsson (Senior Member, IEEE) received the M.Sc. degree in electrical engineering and the Ph.D. degree in automatic control from LTH, Lund University, Lund, Sweden, in 1992 and 1999, respectively. He was appointed as a Docent in 2005 and an Excellent Teaching Practitioner in 2007. Since 2012, he has been a Full Professor with the Department of Automatic Control, LTH, Lund University, Sweden. His research interests include nonlinear estimation and control, robotics research on mobile and industrial manipulators, and feedback control of computing systems
Corresponding author: Zhiyong Geng, e-mail: zygeng@pku.edu.cn
Received Date: 2021-03-27
Revised Date: 2021-06-06
Accepted Date: 2021-08-01

Available Online: 2021-08-29

Abstract

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 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.
- Exponential stabilization,
- logarithmic feedback,
- matrix Lie group,
- underactuated vehicle

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References(33)

References

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The vehicle investigated in this paper is an underactuated system, which has six degrees of freedom but only four independent control inputs
The model of the underactuated vehicle is established on the matrix Lie group SE(3), which describes the rigid body’s configuration globally and uniquely
Two additional rotation matrices are constructed to generate a motion of rotation coupled with translation, so that the underactuated states can be driven by the control inputs
The control law can exponentially stabilize the underactuated vehicle with almost global domain of convergence, that is, any point on SE(3) except for several ones with measure zero

Exponential Set-Point Stabilization of Underactuated Vehicles Moving in Three-Dimensional Space

doi: 10.1109/JAS.2021.1004323

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