Authors

Zihao Song, Panos J. Antsaklis, Hai Lin

Abstract

Rigid body platoons are widely applied in many scenarios, such as planar vehicular platoons, satellite networks, and aerial/underwater navigation formations. Like string stability, mesh stability is adopted in these higher dimensional platoons to capture the non-increasing tracking errors over the networks. In this letter, we extend the traditional vehicular platooning control to higher dimensional rigid body scenarios with mesh stability concerns. The main challenges stem from the inherent underactuation of rigid body dynamics, the nonlinearity introduced by the \( SO\textit {(}3\textit {)} \)-based rotations, and the maintenance of mesh stability for all formations. To this end, we first apply the notion of \( l_{2} \) weak mesh stability to capture the effect of propagation of errors over the network. Then, by assuming all the followers have access to the leader’s information, we propose a novel and constructive rigid body platooning control method based on the port-Hamiltonian framework, which also guarantees the \( l_{2} \) weak mesh stability. This designed controller is further refined for the case when each follower only knows the neighboring information. Finally, the effectiveness of the proposed methods is verified via numerical simulations.

Citation

  • Journal: IEEE Control Systems Letters
  • Year: 2024
  • Volume: 8
  • Issue:
  • Pages: 2805–2810
  • Publisher: Institute of Electrical and Electronics Engineers (IEEE)
  • DOI: 10.1109/lcsys.2024.3516672

BibTeX

@article{Song_2024,
  title={{Port-Hamiltonian-Based Geometric Control for Rigid Body Platoons With Mesh Stability Guarantee}},
  volume={8},
  ISSN={2475-1456},
  DOI={10.1109/lcsys.2024.3516672},
  journal={IEEE Control Systems Letters},
  publisher={Institute of Electrical and Electronics Engineers (IEEE)},
  author={Song, Zihao and Antsaklis, Panos J. and Lin, Hai},
  year={2024},
  pages={2805--2810}
}

Download the bib file

References

  • Feng, S. et al. String stability for vehicular platoon control: Definitions and analysis methods. Annual Reviews in Control vol. 47 81–97 (2019) – 10.1016/j.arcontrol.2019.03.001
  • Stüdli, S., Seron, M. M. & Middleton, R. H. From vehicular platoons to general networked systems: String stability and related concepts. Annual Reviews in Control vol. 44 157–172 (2017) – 10.1016/j.arcontrol.2017.09.016
  • Do, H. et al. Formation Control Algorithms for Multiple-UAVs: A Comprehensive Survey. EAI Endorsed Transactions on Industrial Networks and Intelligent Systems vol. 8 170230 (2021) – 10.4108/eai.10-6-2021.170230
  • Beckers, T., Pappas, G. J. & Colombo, L. J. Learning Rigidity-based Flocking Control using Gaussian Processes with Probabilistic Stability Guarantees. 2022 IEEE 61st Conference on Decision and Control (CDC) 7254–7259 (2022) doi:10.1109/cdc51059.2022.9992465 – 10.1109/cdc51059.2022.9992465
  • Yu, Y., Guo, J., Ahn, C. K. & Xiang, Z. Neural Adaptive Distributed Formation Control of Nonlinear Multi-UAVs With Unmodeled Dynamics. IEEE Transactions on Neural Networks and Learning Systems vol. 34 9555–9561 (2023) – 10.1109/tnnls.2022.3157079
  • Zhao, L., Wen, S., Li, C., Shi, K. & Huang, T. A Recent Survey on Control for Synchronization and Passivity of Complex Networks. IEEE Transactions on Network Science and Engineering vol. 9 4235–4254 (2022) – 10.1109/tnse.2022.3196786
  • Roza, Motion control of rigid bodies in SE (3). (2012)
  • Sontag, E. D. & Wang, Y. On characterizations of the input-to-state stability property. Systems & Control Letters vol. 24 351–359 (1995) – 10.1016/0167-6911(94)00050-6
  • Lee, T., Leok, M. & McClamroch, N. H. Geometric tracking control of a quadrotor UAV on SE(3). 49th IEEE Conference on Decision and Control (CDC) 5420–5425 (2010) doi:10.1109/cdc.2010.5717652 – 10.1109/cdc.2010.5717652
  • Duong, T. & Atanasov, N. Hamiltonian-based Neural ODE Networks on the SE(3) Manifold For Dynamics Learning and Control. Robotics: Science and Systems XVII (2021) doi:10.15607/rss.2021.xvii.086 – 10.15607/rss.2021.xvii.086
  • An Invariance Principle in the Theory of Stability. Control Theory (2009) doi:10.1109/9780470544334.ch16 – 10.1109/9780470544334.ch16
  • Liang, X., Fang, Y., Sun, N. & Lin, H. A Novel Energy-Coupling-Based Hierarchical Control Approach for Unmanned Quadrotor Transportation Systems. IEEE/ASME Transactions on Mechatronics vol. 24 248–259 (2019) – 10.1109/tmech.2019.2891083
  • Amirkhani, A. & Barshooi, A. H. Consensus in multi-agent systems: a review. Artificial Intelligence Review vol. 55 3897–3935 (2021) – 10.1007/s10462-021-10097-x