Skip to main content
SpringerLink
Log in

Fixed-time Localization of Local Coordinate Frames: Interpretation and Applications to Formation Control Problems

International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Cite this article

Abstract

This paper proposes a fixed-time (FxT) frame (or pose) localization scheme for multi-agent systems based on the inter-agent relative poses specified by SE(3) transformation matrices. Under the localization law, the agents’ local coordinate frames are localized almost globally in fixed-time with regard to a common reference frame. Based on the FxT frame estimation, the SE(3) formation control for multi-agent systems with connected graphs can be simply cast as the stabilization in SE(3) for each individual agent. When the desired formation is specified by the desired inter-agent bearing vectors, FxT bearing-based formation control is presented with no need for the global reference frame common to the agents. Simulation results are provided to support the theoretical development.

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

Similar content being viewed by others

References

  1. Q. V. Tran and H.-S. Ahn, “Multi-agent localization of a common reference coordinate frame: An extrinsic approach,” IFAC-PapersOnLine, vol. 52, no. 20, pp. 67–72, 2019.

    Article  Google Scholar 

  2. A. Sarlette, R. Sepulchre, and N. E. Leonard, “Autonomous rigid body attitude synchronization,” Automatica, vol. 45, pp. 572–577, 2009.

    Article  MathSciNet  MATH  Google Scholar 

  3. J. Thunberg, F. Bernard, and J. Goncalves, “Distributed methods for synchronization of orthogonal matrices over graphs,” Automatica, vol. 80, pp. 243–252, 2017.

    Article  MathSciNet  MATH  Google Scholar 

  4. J. Markdahl, J. Thunberg, and J. Goncalves, “Almost global consensus on the n-sphere,” IEEE Transactions on Automatic Control, vol. 63, no. 6, pp. 1664–1675, 2018.

    Article  MathSciNet  MATH  Google Scholar 

  5. H. Gui and A. H. J. de Ruiter, “Global finite-time attitude consensus of leader-following spacecraft systems based on distributed observers,” Automatica, vol. 91, pp. 225–232, 2018.

    Article  MathSciNet  MATH  Google Scholar 

  6. Q. Zong and S. Shao, “Decentralized finite-time attitude synchronization for multiple rigid spacecraft via a novel disturbance observer,” ISA Transactions, vol. 65, pp. 150–163, 2016.

    Article  Google Scholar 

  7. J. Wei, S. Zhang, A. Adaldo, J. Thunberg, X. Hu, and K. H. Johansson, “Finite-time attitude synchronization with distributed discontinuous protocols,” IEEE Transactions on Automatic Control, vol. 63, no. 10, pp. 3608–3615, 2018.

    Article  MathSciNet  MATH  Google Scholar 

  8. R. Tron and R. Vidal, “Distributed 3-D localization of camera sensor networks from 2-D image measurements,” IEEE Transactions on Automatic Control, vol. 59, no. 12, pp. 3325–3340, 2014.

    Article  MathSciNet  MATH  Google Scholar 

  9. Q. V. Tran, H.-S. Ahn, and B. D. O. Anderson, “Distributed orientation localization of multi-agent systems in 3-dimensional space with direction-only measurements,” in Proc. 57th IEEE Confer. Decision Control (CDC), pp. 2883–2889, 2018.

  10. Q. V. Tran, M. H. Trinh, D. Zelazo, D. Mukherjee, and H.-S. Ahn, “Finite-time bearing-only formation control via distributed global orientation estimation,” IEEE Transactions on Control of Network Systems, vol. 2, no. 6, pp. 702–712, 2019.

    Article  MathSciNet  MATH  Google Scholar 

  11. J.-G. Lee, Q. V. Tran, K.-H. Oh, P.-G. Park, and H.-S. Ahn, “Distributed object pose estimation over strongly connected networks,” Systems & Control Letters, vol. 175, p. 105505, 2023.

    Article  MathSciNet  MATH  Google Scholar 

  12. Y. Igarashi, T. Hatanaka, M. Fujita, and M. W. Spong, “Passivity-based attitude synchronization in SE(3),” IEEE Transactions on Control Systems Technology, vol. 17, pp. 1119–1134, 2009.

    Article  Google Scholar 

  13. S. Zhao and D. Zelazo, “Bearing rigidity and almost global bearing-only formation stabilization,” IEEE Transactions on Automatic Control, vol. 61, no. 5, pp. 1255–1268, 2015.

    Article  MathSciNet  MATH  Google Scholar 

  14. J. Zhao, X. Yu, X. Li, and H. Wang, “Bearing-only formation tracking control of multi-agent systems with local reference frames and constant-velocity leaders,” IEEE Control Systems Letters, vol. 5, no. 1, pp. 1–6, 2021.

    Article  MathSciNet  Google Scholar 

  15. Q. V. Tran, H.-S. Ahn, and J. Kim, “Direction-only orientation alignment of leader-follower networks,” Proc. of the 2022 American Control Conference (ACC), 2022, pp. 2142–2147.

  16. K.-K. Oh and H.-S. Ahn, “Distributed formation control based on orientation alignment and position estimation,” International Journal of Control, Automation, and Systems, vol. 16, pp. 1112–1119, 2018.

    Article  Google Scholar 

  17. J. Thunberg, J. Goncalves, and X. Hu, “Consensus and formation control on SE(3) for switching topologies,” Automatica, vol. 66, pp. 109–121, 2016.

    Article  MathSciNet  MATH  Google Scholar 

  18. C. K. Verginis, A. Nikou, and D. V. Dimarogonas, “Robust formation control in SE(3) for tree-graph structures with prescribed transient and steady state performance,” Automatica, vol. 103, pp. 538–548, 2019.

    Article  MathSciNet  MATH  Google Scholar 

  19. X. Peng, J. Sun, and Z. Geng, “The geometric convexity on SE(3) and its application to the formation tracking in multivehicle systems,” International Journal of Control, vol. 92, no. 3, pp. 528–539, 2019.

    Article  MathSciNet  MATH  Google Scholar 

  20. F. Arrigoni, A. Fusiello, R. Rizzi, E. Ricci, and T. Pajdla, “Revisiting viewing graph solvability: An effective approach based on cycle consistency,” IEEE Transactions on Pattern Analysis and Machine Intelligence, pp. 1–14, 2022. DOI: https://doi.org/10.1109/TPAMI.2022.3212595

  21. L. An and G.-H. Yang, “Distributed optimal coordination for heterogeneous linear multiagent systems,” IEEE Transactions on Automatic Control, vol. 67, no. 12, pp. 6850–6857, 2022.

    Article  MathSciNet  MATH  Google Scholar 

  22. S. Bhat and D. Bernstein, “Finite-time stability of continuous autonomous systems,” SIAM Journal on Control and Optimization, vol. 38, no. 3, pp. 751–766, 2000.

    Article  MathSciNet  MATH  Google Scholar 

  23. S. Parsegov, A. Polyakov, and P. Shcherbakov, “Fixed-time consensus algorithm for multi-agent systems with integrator dynamics,” IFAC Proceedings Volumes, vol. 46, no. 27, pp. 110–115, 2013.

    Article  Google Scholar 

  24. A. Polyakov, “Nonlinear feedback design for fixed-time stabilization of linear control systems,” IEEE Transactions on Automatic Control, vol. 57, no. 8, pp. 2106–2110, 2012.

    Article  MathSciNet  MATH  Google Scholar 

  25. Q. V. Tran and H.-S. Ahn, “Distributed formation control of mobile agents via global orientation estimation,” IEEE Transactions on Control of Network Systems, vol. 4, no. 7, pp. 1654–1664, 2020.

    Article  MathSciNet  MATH  Google Scholar 

  26. M. H. Trinh, D. Mukherjee, D. Zelazo, and H.-S. Ahn, “Finite-time bearing-only formation control,” Proc. of 56th IEEE Confer. Decision Control (CDC), 2017, pp. 1578–1583.

  27. H. K. Khalil, Nonlinear Systems, 3rd ed., Prentice Hall, 2002.

  28. R. Aldana-López, D. Gómez-Gutiérrez, E. Jiménez-Rodríguez, J. D. Sánchez-Torres, and M. Defoort, “Enhancing the settling time estimation of a class of fixed-time stable systems,” International Journal of Robust and Nonlinear Control, vol. 29, no. 12, pp. 4135–4148, 2019.

    Article  MathSciNet  MATH  Google Scholar 

  29. Q. V. Tran, M. H. Trinh, N. H. Nguyen, and H.-S. Ahn, “Free-will arbitrary time consensus protocols with diffusive coupling,” International Journal of Robust and Nonlinear Control, vol. 32, no. 15, pp. 8711–8731, 2022.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechatronics, the School of Mechanical Engineering, Hanoi University of Science and Technology (HUST), Hanoi, Vietnam

    Quoc Van Tran

Authors
  1. Quoc Van Tran
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Quoc Van Tran.

Ethics declarations

The author declares 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.

This work is funded by Hanoi University of Science and Technology (HUST) under project number T2022-TT-004. Early version of this work was presented at the 8th IFAC Workshop on Distributed Estimation and Control in Networked Systems [1].

Quoc Van Tran is a Lecturer with the Department of Mechatronics, the School of Mechanical Engineering, Hanoi University of Science and Technology (HUST), Hanoi, Vietnam. He received his B.E. degree in mechatronics from HUST in 2013, and an M.S. degree in mechatronics and a Ph.D. degree in mechanical engineering both from Gwangju Institute of Science and Technology (GIST), Gwangju, Korea, in 2015 and 2021, respectively. Before joining HUST, he was a Postdoctoral Researcher with the Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Korea. Dr. Tran serves as an Associate Editor for the International Journal of Control, Automation, and Systems (IJCAS). His research interests include networked system, distributed optimization, and robotics.

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Van Tran, Q. Fixed-time Localization of Local Coordinate Frames: Interpretation and Applications to Formation Control Problems. Int. J. Control Autom. Syst. 21, 4057–4066 (2023). https://doi.org/10.1007/s12555-023-0113-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-023-0113-4

Keywords

search

Navigation