Skip to main content
SpringerLink
Log in

Consensus Control of Rigid Body Spacecraft in Orbital Relative Motion using TSE(3) and Exponential Coordinates

  • Original Article
  • Published:
The Journal of the Astronautical Sciences Aims and scope Submit manuscript

Abstract

In this paper, two consensus control algorithms are proposed for control of multi-agent rigid body spacecraft in orbital relative motion. In the first approach, a proportional-derivative (PD) consensus control method, an extension of the Morse-Lyapunov analysis in the framework of the tangent bundle TSE(3) associated with Lie group SE(3) is used where rotation matrices parameterize the attitude of the rigid bodies. In the second approach, a proportional-integral-derivative (PID) consensus control protocol is introduced where the configurations of the rigid bodies are described in terms of the exponential coordinates associated with the Lie group SE(3). The control objective is to stabilize the relative pose configurations with velocity synchronization of the spacecraft which share their states according to a static communication topology in the presence of gravitational forces and torques. Finally, simulation examples are given to demonstrate the proposed methods.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  1. Ren, W., Beard, R.W.: Distributed Consensus in Multi-vehicle Cooperative Control. Springer, Berlin (2008)

    Book  Google Scholar 

  2. Sarlette, A., Sepulchre, R., Leonard, N.E.: Autonomous rigid body attitude synchronization. Automatica 45(2), 572–577 (2009)

    Article  MathSciNet  Google Scholar 

  3. Maadani, M., Butcher, E.A., Nazari, M., Yucelen, T.: Decentralized consensus control of rigid bodies using exponential coordinates. In: AIAA Scitech 2019 Forum, p. 1161 (2019)

  4. Maadani, M., Butcher, E.A., Sanyal, A.K.: Finite-time attitude consensus control of a multi-agent rigid body system. In: American Control Conference (ACC), IEEE, 2020, pp 877–882 (2020)

  5. Zou, Y., Meng, Z.: Velocity-free leader–follower cooperative attitude tracking of multiple rigid bodies on SO(3). IEEE Trans. Cybern. 49(12), 4078–4089 (2018)

    Article  Google Scholar 

  6. Chen, T., Shan, J.: Continuous constrained attitude regulation of multiple spacecraft on SO(3). Aerosp. Sci. Technol. 99, 105769 (2020)

    Article  Google Scholar 

  7. Chen, T.: Continuous leaderless synchronization control of multiple spacecraft on SO(3). Astrodynamics 5(3), 279–291 (2021)

    Article  Google Scholar 

  8. Dong, R., Geng, Z.: Consensus based formation control laws for systems on Lie groups. Syst. Control Lett. 62, 104–111 (2013)

    Article  MathSciNet  Google Scholar 

  9. Zhang, J., Ye, D., Liu, M., Sun, Z.: Adaptive fuzzy finite-time control for spacecraft formation with communication delays and changing topologies. J. Franklin Inst. 354(11), 4377–4403 (2017)

    Article  MathSciNet  Google Scholar 

  10. Junkins, J.L., Schaub, H.: Analytical mechanics of space systems. American Institute of Aeronautics and Astronautics (2009)

  11. Clohessy, W.H., Wiltshire, R.S.: Terminal guidance system for satellite rendezvous. J. Aerosp. Sci. 27(9), 653–658 (1960)

    Article  Google Scholar 

  12. London, H.S.: Second approximation to the solution of the rendezvous equations. AIAA J. 1(7), 1691–1693 (1963)

    Article  Google Scholar 

  13. De Vries, J.P.: Elliptic elements in terms of small increments of position and velocity components. AIAA J. 1(11), 2626–2629 (1963)

    Article  Google Scholar 

  14. Anthony, M.L., Sasaki, F.T.: Rendezvous problem for nearly circular orbits. AIAA J. 3(9), 1666–1673 (1965)

    Article  Google Scholar 

  15. Vaddi, S.S., Vadali, S.R., Alfriend, K.T.: Formation flying: Accommodating nonlinearity and eccentricity perturbations. J. Guid. Control Dyn. 26 (2), 214–223 (2003)

    Article  Google Scholar 

  16. Bohn, J., Sanyal, A.K.: Almost global finite-time stabilization of rigid body attitude dynamics using rotation matrices. Int. J. Robust Nonlinear Control 26(9), 2008–2022 (2016)

    Article  MathSciNet  Google Scholar 

  17. Nazari, M., Maadani, M., Butcher, E.A., Yucelen, T.: Morse-Lyapunov-based control of rigid body motion on TSE(3) via backstepping. In: 2018 AIAA Guidance, Navigation, and Control Conference, p 0602 (2018)

  18. Maadani, M., Butcher, E.A.: PID Pose consensus control of a multi-agent rigid body system using exponential coordinates. In: AIAA SCITECH 2022 Forum, 2022, p 0767 (2022)

  19. Lee, D., Sanyal, A.K., Butcher, E.A.: Asymptotic tracking control for spacecraft formation flying with decentralized collision avoidance. J. Guid. Control Dyn. 38(4), 587–600 (2015)

    Article  Google Scholar 

  20. Butcher, E.A., Maadani, M.: Morse-lyapunov-based decentralized consensus control of rigid body spacecraft in orbital relative motion. In: The 2019 AAS/AIAA Astrodynamics Specialist Conference, AAS, pp. 19–713 (2019)

  21. Chaturvedi, N.A., Sanyal, A.K., McClamroch, N.H.: Rigid-Body Attitude control. IEEE Control Syst. Mag. 31(3), 30–51 (2011)

    Article  Google Scholar 

  22. Butcher, E.A., Maadani, M.: Consensus control of a multi-agent rigid body system on TSO(3)N and TSE(3)N. In: 2019 Sixth Indian Control Conference (ICC), pp. 98–103 (2019)

  23. Crnkić, A., Jaćimović, V.: Consensus and balancing on the three-sphere. J. Glob. Optim. 76(3), 575–586 (2020)

    Article  MathSciNet  Google Scholar 

  24. Khalil, H.K.: Nonlinear Systems, 3rd ed. Prentice-Hall (2002)

    MATH  Google Scholar 

  25. Dimarogonas, D.V., Tsiotras, P., Kyriakopoulos, K.J.: Laplacian cooperative attitude control of multiple rigid bodies. In: 2006 IEEE Conference on Computer Aided Control System Design, 2006 IEEE International Conference on Control Applications, 2006 IEEE International Symposium on Intelligent Control, pp 3064–3069 (2006)

  26. Maadani, M., Butcher, E.A.: 6-DOF Consensus control of multi-agent rigid body systems using rotation matrices. Int. J. Control 0(0), 1–15 (2021). https://doi.org/10.1080/00207179.2021.1928291

    Article  Google Scholar 

  27. Mukherjee, R., Chen, D.: Asymptotic stability theorem for autonomous systems. J. Guid. Control Dyn. 16(5), 961–963 (1993)

    Article  Google Scholar 

  28. Nazari, M., Butcher, E.A., Yucelen, T., Sanyal, A.K.: Decentralized consensus control of a rigid-body spacecraft formation with communication delay. J. Guid. Control Dyn. 39(4), 838–851 (2016)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, Rutgers University, Piscataway, NJ, 08854, USA

    Mohammad Maadani

  2. Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, AZ, 85721, USA

    Eric A. Butcher

Authors
  1. Mohammad Maadani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Eric A. Butcher
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Eric A. Butcher.

Ethics declarations

Conflict of Interests

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Maadani, M., Butcher, E.A. Consensus Control of Rigid Body Spacecraft in Orbital Relative Motion using TSE(3) and Exponential Coordinates. J Astronaut Sci 69, 801–828 (2022). https://doi.org/10.1007/s40295-022-00322-2

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40295-022-00322-2

Search

Navigation