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Stabilization of coupled orbit–attitude dynamics about an asteroid utilizing Hamiltonian structure

A Correction to this article was published on 11 February 2022

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Abstract

The gravitationally coupled orbit–attitude dynamics, also called the full dynamics, in which the spacecraft is modeled as a rigid body, is a high-precision model for the motion in the close proximity of an asteroid. A feedback control law is proposed to stabilize relative equilibria of the coupled orbit–attitude motion in a uniformly rotating second degree and order gravity field by utilizing the Hamiltonian structure. The feedback control law is consisted of potential shaping and energy dissipation. The potential shaping makes the relative equilibrium a minimum of the modified Hamiltonian by modifying the potential artificially. With the energy-Casimir method, it is theoretically proved that an unstable relative equilibrium can always be stabilized in the Lyapunov sense by the potential shaping with sufficiently large feedback gains. Then, the energy dissipation leads the motion to converge to the relative equilibrium. The proposed stabilization control law has a simple form and is easy to implement autonomously, which can be attributed to the utilization of natural dynamical behaviors in the controller design.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant Nos. 11432001 and 11602009, and the Fundamental Research Funds for the Central Universities.

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Correspondence to Yue Wang.

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Yue Wang received his B.Eng. and Ph.D. degrees in aerospace engineering from Beihang University (formerly known as Beijing University of Aeronautics and Astronautics), Beijing, China, in 2009 and 2014, respectively. From 2014 to 2015, he worked as a postdoctoral fellow in the Distributed Space Systems Lab in the Faculty of Aerospace Engineering at Technion–Israel Institute of Technology, Haifa, Israel. In 2016, he joined the School of Astronautics at Beihang University as an associate professor of the “Zhuoyue” Recruitment Program. His research interests center on the astrodynamics, orbital dynamics, dynamics and control about asteroids, proximity operations, and space debris mitigation.

Shijie Xu received his B.Eng. degree from the Department of Mechanical Engineering, Northeast Forestry University, Harbin, China, in 1976, M.S. degree from the Laboratory of Flight Dynamics, Harbin Institute of Technology, Harbin, China, in 1983, and Ph.D. degree with a specialization in automatic controls from Henri Poincaré University, Nancy, France, in 1995. From 1989 to 2000, he was with Harbin Institute of Technology, where he was an associate professor and then a professor. In 2000, he joined the School of Astronautics, Beihang University, Beijing, China, where he is currently a professor. He has authored or coauthored over 300 papers in journals and conferences. His research interests include robust control, astrodynamics, spacecraft guidance, navigation and control, and deep space exploration. He was a recipient of the Key Program Funding of the National Natural Science Foundation of China from 2015 to 2019.

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Wang, Y., Xu, S. Stabilization of coupled orbit–attitude dynamics about an asteroid utilizing Hamiltonian structure. Astrodyn 2, 53–67 (2018). https://doi.org/10.1007/s42064-017-0013-6

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  • DOI: https://doi.org/10.1007/s42064-017-0013-6

Keywords

  • asteroid missions
  • gravitationally coupled orbit–attitude dynamics
  • full dynamics
  • stabilization
  • non-canonical Hamiltonian
  • structure
  • potential shaping