Angle formation of double integrator with bearing and velocity information

Authors

Ningbo Li, Pablo Borja, Arjan van der Schaft, Jacquelien M.A. Scherpen, Liangming Chen

Abstract

This paper proposes a passivity-based approach using bearing and velocity information for a triangular formation control with the interaction topology constrained by angles. The controller framework is designed using virtual couplings on the relative measurements related to the edges. The different measurements associated with the edges are mapped by the measurement Jacobian, which is calculated by the time-evolution of the measurement. To avoid unavailable distance measurements in the control law, an estimator is designed based on port-Hamiltonian theory using bearing and velocity measurements. The stability analysis of the closed-loop system is provided and simulations are performed to illustrate the effectiveness of the approach.

Keywords

Angle formation; double integrator; port-Hamiltonian; distance estimator

Citation

• Journal: IFAC-PapersOnLine
• Year: 2021
• Volume: 54
• Issue: 19
• Pages: 217–222
• Publisher: Elsevier BV
• DOI: 10.1016/j.ifacol.2021.11.081
• Note: 7th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2021- Berlin, Germany, 11-13 October 2021

BibTeX

@article{Li_2021,
  title={{Angle formation of double integrator with bearing and velocity information}},
  volume={54},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2021.11.081},
  number={19},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Li, Ningbo and Borja, Pablo and van der Schaft, Arjan and Scherpen, Jacquelien M.A. and Chen, Liangming},
  year={2021},
  pages={217--222}
}

Download the bib file

References

• Rigid graph control architectures for autonomous formations. IEEE Control Systems vol. 28 48–63 (2008) – 10.1109/mcs.2008.929280
• Cao, M., Yu, C. & Anderson, B. D. O. Formation control using range-only measurements. Automatica vol. 47 776–781 (2011) – 10.1016/j.automatica.2011.01.067
• Chen, L., Cao, M. & Li, C. Angle Rigidity and Its Usage to Stabilize Multiagent Formations in 2-D. IEEE Transactions on Automatic Control vol. 66 3667–3681 (2021) – 10.1109/tac.2020.3025539
• Duindam, (2009)
• Jing, G., Zhang, G., Lee, H. W. J. & Wang, L. Angle-based shape determination theory of planar graphs with application to formation stabilization. Automatica vol. 105 117–129 (2019) – 10.1016/j.automatica.2019.03.026
• Stacey, A passivity-based approach to formation control using partial measurements of relative position. IEEE Transactions on Automatic Control (2015)
• Trinh, Bearing-based formation control of a group of agents with leader-first follower structure. IEEE Transactions on Automatic Control (2018)
• van der Schaft, A. & Jeltsema, D. Port-Hamiltonian Systems Theory: An Introductory Overview. Foundations and Trends® in Systems and Control vol. 1 173–378 (2014) – 10.1561/2600000002
• Vos, E., Scherpen, J. M. A., Schaft, A. J. van der & Postma, A. Formation Control of Wheeled Robots in the Port-Hamiltonian Framework. IFAC Proceedings Volumes vol. 47 6662–6667 (2014) – 10.3182/20140824-6-za-1003.00394
• Xu, M. & Liang, Y. Formation Flying on Elliptic Orbits by Hamiltonian Structure-Preserving Control. Journal of Guidance, Control, and Dynamics vol. 41 294–300 (2018) – 10.2514/1.g002141
• Zhao, S., Li, Z. & Ding, Z. Bearing-Only Formation Tracking Control of Multiagent Systems. IEEE Transactions on Automatic Control vol. 64 4541–4554 (2019) – 10.1109/tac.2019.2903290