Skip to main content
SpringerLink
Log in

A Consensus-Based Model Predictive Control with Optimized Line-of-Sight Guidance for Formation Trajectory Tracking of Autonomous Underwater Vehicles

  • Short paper
  • Published:
Journal of Intelligent & Robotic Systems Aims and scope Submit manuscript

Abstract

This paper investigates the leader-follower formation control problem of underactuated autonomous underwater vehicles. To solve the issues of inputs constraint and partial communication blocked between the leader and the followers, a novel consensus-based model predictive control scheme with optimized line-of-sight guidance is proposed. A desired optimal heading is generated by the line-of-sight guidance with reference governor, which is instrumented to compensate for the lack of actuator in sway direction. The reference governor is employed to prescribe the increment of desired optimal heading by balancing the line-of-sight guidance law and current heading. The information from the leader and neighbors is integrated using graph theory based on consensus scheme, which reduces the dependency of the leader compared to traditional leader-follower formation methods. The relative distances between followers are used to design state constraints for collision avoidance. Meanwhile, when the communication between the leader and the followers is partially blocked, the proposed controller can still generate the optimal control inputs and guarantee the formation tracking performance relying on the neighbors’ state. An auxiliary Lyapunov-based contraction constraint is implemented to guarantee the stability. Finally, numerical simulations are provided to demonstrate the effectiveness and robustness of the proposed controller.

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

Data Availability

Not applicable.

References

  1. Lu, Y., Zhang, G., Sun, Z., Zhang, W.: Robust adaptive formation control of underactuated autonomous surface vessels based on MLP and DOB. Nonlinear Dyn. 94, 503–519 (2018). https://doi.org/10.1007/s11071-018-4374-z

    Article  MATH  Google Scholar 

  2. Shen, C., Shi, Y., Buckham, B.: Trajectory tracking control of an autonomous underwater vehicle using Lyapunov-based model predictive control. IEEE Trans. Ind. Electron. 65, 5796–5805 (2018). https://doi.org/10.1109/TIE.2017.2779442

    Article  Google Scholar 

  3. Wang, J., Wang, C., Wei, Y., Zhang, C.: Neuroadaptive sliding mode formation control of autonomous underwater vehicles with uncertain dynamics. IEEE Syst. J. 14, 3325–3333 (2020). https://doi.org/10.1109/JSYST.2019.2938315

    Article  Google Scholar 

  4. Shojaei, K.: Neural network formation control of underactuated autonomous underwater vehicles with saturating actuators. Neurocomputing. 194, 372–384 (2016). https://doi.org/10.1016/j.neucom.2016.02.041

    Article  Google Scholar 

  5. Sun, Z., Zhang, G., Lu, Y., Zhang, W.: Leader-follower formation control of underactuated surface vehicles based on sliding mode control and parameter estimation. ISA Trans. 72, 15–24 (2018). https://doi.org/10.1016/j.isatra.2017.11.008

    Article  Google Scholar 

  6. Peng, Z., Wang, D., Chen, Z., Hu, X., Lan, W.: Adaptive dynamic surface control for formations of autonomous surface vehicles with uncertain dynamics. IEEE Trans. Control Syst. Technol. 21, 513–520 (2013). https://doi.org/10.1109/TCST.2011.2181513

    Article  Google Scholar 

  7. Peng, Z., Wen, G., Rahmani, A., Yu, Y.: Leader–follower formation control of nonholonomic mobile robots based on a bioinspired neurodynamic based approach. Rob. Auton. Syst. 61, 988–996 (2013). https://doi.org/10.1016/j.robot.2013.05.004

    Article  Google Scholar 

  8. Edwards, D.B., Bean, T.A., Odell, D.L., Anderson, M.J.: A leader-follower algorithm for multiple AUV formations. In: 2004 IEEE/OES autonomous underwater vehicles (IEEE Cat. No.04CH37578). pp. 40–46., Sebasco, ME, USA (2004)

  9. Hu, Z., Ma, C., Zhang, L., Halme, A., Hayat, T., Ahmad, B.: Formation control of impulsive networked autonomous underwater vehicles under fixed and switching topologies. Neurocomputing. 147, 291–298 (2015). https://doi.org/10.1016/j.neucom.2014.06.060

    Article  Google Scholar 

  10. GAO, Z.: Fixed-time leader-follower formation control of autonomous underwater vehicles with event-triggered intermittent communications. IEEE Access. 6, 27902–27911 (2018)

    Article  Google Scholar 

  11. Ge, X., Han, Q.-L.: Distributed formation control of networked multi-agent systems using a dynamic event-triggered communication mechanism. IEEE Trans. Ind. Electron. 64, 8118–8127 (2017). https://doi.org/10.1109/TIE.2017.2701778

    Article  Google Scholar 

  12. Li, J., Du, J., Chang, W.-J.: Robust time-varying formation control for underactuated autonomous underwater vehicles with disturbances under input saturation.pdf. Ocean Eng. 9 (2019)

  13. Yan, Z., Xu, D., Chen, T., Zhang, W., Liu, Y.: Leader-follower formation control of UUVs with model uncertainties, current disturbances, and unstable communication. Sensors. 18, 662 (2018). https://doi.org/10.3390/s18020662

    Article  Google Scholar 

  14. Huang, H., Zhu, D., Ding, F.: Dynamic task assignment and path planning for Multi-AUV system in variable ocean current environment. J. Intell. Rob. Syst. 74, 999–1012 (2014). https://doi.org/10.1007/s10846-013-9870-2

    Article  Google Scholar 

  15. Li, X.: An adaptive SOM neural network method for distributed formation control of a group of AUVs. IEEE Trans. Ind. Electron. 65, 11 (2018)

    Google Scholar 

  16. Zhang, J., Xiang, X., Zhang, Q., Li, W.: Neural network-based adaptive trajectory tracking control of underactuated AUVs with unknown asymmetrical actuator saturation and unknown dynamics. Ocean Eng. 218, 108193 (2020). https://doi.org/10.1016/j.oceaneng.2020.108193

    Article  Google Scholar 

  17. Liu, C., Negenborn, R.R., Chu, X., Zheng, H.: Predictive path following based on adaptive line-of-sight for underactuated autonomous surface vessels. J. Mar. Sci. Technol. 23, 483–494 (2018). https://doi.org/10.1007/s00773-017-0486-2

    Article  Google Scholar 

  18. Peng, Z., Wang, J.: Output-feedback path-following control of autonomous underwater vehicles based on an extended state observer and projection neural networks. IEEE Trans. Syst. Man Cybern.: Syst. 48, 535–544 (2018). https://doi.org/10.1109/TSMC.2017.2697447

    Article  Google Scholar 

  19. Peng, Z., Wang, J., Han, Q.-L.: Path-following control of autonomous underwater vehicles subject to velocity and input constraints via neurodynamic optimization. IEEE Trans. Ind. Electron. 66, 8724–8732 (2019). https://doi.org/10.1109/TIE.2018.2885726

    Article  Google Scholar 

  20. Zheng, H., Wu, J., Wu, W., Zhang, Y.: Robust dynamic positioning of autonomous surface vessels with tube-based model predictive control. Ocean Eng. 199, 106820 (2020). https://doi.org/10.1016/j.oceaneng.2019.106820

    Article  Google Scholar 

  21. Zheng, H., Negenborn, R.R., Lodewijks, G.: Robust distributed predictive control of waterborne AGVs—A cooperative and cost-effective approach. IEEE Trans. Cybern. 48, 2449–2461 (2018). https://doi.org/10.1109/TCYB.2017.2740558

    Article  Google Scholar 

  22. Zheng, H., Wu, J., Wu, W., Negenborn, R.R.: Cooperative distributed predictive control for collision-free vehicle platoons. IET Intell. Transp. Syst. 13, 816–824 (2019). https://doi.org/10.1049/iet-its.2018.5366

    Article  Google Scholar 

  23. Zheng, H., Negenborn, R.R., Lodewijks, G.: Fast ADMM for distributed model predictive control of cooperative waterborne AGVs. IEEE Trans. Control Syst. Technol. 25, 1406–1413 (2017). https://doi.org/10.1109/TCST.2016.2599485

    Article  Google Scholar 

  24. Zheng, H., Negenborn, R.R., Lodewijks, G.: Predictive path following with arrival time awareness for waterborne AGVs. Transp. Res. Part C: Emerg. Technol. 70, 214–237 (2016). https://doi.org/10.1016/j.trc.2015.11.004

    Article  Google Scholar 

  25. Li, H.: On neighbor information utilization in distributed receding horizon control for consensus-seeking. IEEE Trans. Cybern. 46, 9 (2016)

    Article  Google Scholar 

  26. Li, H., Yan, W.: Receding horizon control based consensus scheme in general linear multi-agent systems. Automatica. 56, 12–18 (2015). https://doi.org/10.1016/j.automatica.2015.03.023

    Article  MathSciNet  MATH  Google Scholar 

  27. Li, H., Shi, Y.: Distributed receding horizon control of large-scale nonlinear systems: Handling communication delays and disturbances. Automatica. 50, 1264–1271 (2014). https://doi.org/10.1016/j.automatica.2014.02.031

    Article  MathSciNet  MATH  Google Scholar 

  28. Kuriki, Y., Namerikawa, T.: Formation control with collision avoidance for a multi-UAV system using decentralized MPC and consensus-based control. In: European Control Conference (ECC). pp.3079–3084., Linz, Austria (2015)

  29. Li, J.-H., Lee, P.-M., Jun, B.-H., Lim, Y.-K.: Point-to-point navigation of underactuated ships. Automatica. 44, 3201–3205 (2008). https://doi.org/10.1016/j.automatica.2008.08.003

    Article  MathSciNet  MATH  Google Scholar 

  30. Shojaei, K., Dolatshahi, M.: Line-of-sight target tracking control of underactuated autonomous underwater vehicles. Ocean Eng. 133, 244–252 (2017). https://doi.org/10.1016/j.oceaneng.2017.02.007

    Article  Google Scholar 

  31. Shojaei, K.: 22. Leader–follower formation control of underactuated autonomous marine surface vehicles with limited torque. Ocean Eng. 105, 196–205 (2015). https://doi.org/10.1016/j.oceaneng.2015.06.026

  32. Oh, S.-R., Sun, J.: Path following of underactuated marine surface vessels using line-of-sight based model predictive control. Ocean Eng. 37, 289–295 (2010). https://doi.org/10.1016/j.oceaneng.2009.10.004

    Article  Google Scholar 

  33. Wei, H., Shen, C., Shi, Y.: Distributed Lyapunov-based model predictive formation tracking control for autonomous underwater vehicles subject to disturbances. IEEE Trans. Syst. Man Cybern.: Syst. 51, 5198–5208 (2021). https://doi.org/10.1109/TSMC.2019.2946127

    Article  Google Scholar 

  34. Shen, C., Shi, Y., Buckham, B.: Integrated path planning and tracking control of an AUV: A unified receding horizon optimization approach. IEEE/ASME Trans. Mechatron. 22, 1163–1173 (2017). https://doi.org/10.1109/TMECH.2016.2612689

    Article  Google Scholar 

  35. Pannocchia, G., Rawlings, J.B., Wright, S.J.: Inherently robust suboptimal nonlinear MPC: Theory and application. In: 2011 50th IEEE Conference on Decision and Control and European Control Conference. pp. 3398–3403 (2011)

  36. Shen, C., Shi, Y.: Distributed implementation of nonlinear model predictive control for AUV trajectory tracking. Automatica. 115, (2020). https://doi.org/10.1016/j.automatica.2020.108863

  37. Shen, C., Buckham, B., Shi, Y.: Modified C/GMRES algorithm for fast nonlinear model predictive tracking control of AUVs. IEEE Trans. Control Syst. Technol. 25, 1896–1904 (2017). https://doi.org/10.1109/TCST.2016.2628803

    Article  Google Scholar 

  38. Zheng, H., Negenborn, R.R., Lodewijks, G.: Trajectory tracking of autonomous vessels using model predictive control. IFAC Proc. 47, 8812–8818 (2014). https://doi.org/10.3182/20140824-6-ZA-1003.00767

  39. Diehl, M., Ferreau, H.J., Haverbeke, N.: Efficient Numerical Methods for Nonlinear MPC and Moving Horizon Estimation. In: Magni, L., Raimondo, D.M., Allgöwer, F. (eds.) Nonlinear Model Predictive Control, pp. 391–417. Springer Berlin Heidelberg, Berlin (2009)

    Chapter  Google Scholar 

Download references

Funding

This work was partly supported by the National Natural Science Foundation of China (NSFC) (61971378); Strategic Priority Research Program of the Chinese Academy of Sciences (XDA22030208); Zhoushan-Zhejiang University Joint Research Project (2019C81081).

Author information

Authors and Affiliations

  1. Optical Communications Laboratory, Ocean College, Zhejiang University, Zheda Road 1, Zhoushan, Zhejiang, 316021, China

    Zhonglan Qian, Weichao Lyu, Yizhan Dai & Jing Xu

  2. Key Laboratory of Ocean Observation-Imaging Testbed of Zhejiang Province, Ocean College, Zhejiang University, Zheda Road 1, Zhoushan, Zhejiang, 316021, China

    Zhonglan Qian, Weichao Lyu, Yizhan Dai & Jing Xu

  3. The Engineering Research Center of Oceanic Sensing Technology and Equipment, Ministry of Education, Beijing, China

    Jing Xu

Authors
  1. Zhonglan Qian
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Weichao Lyu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yizhan Dai
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jing Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed to the study conception and design. Design of the work, software, data collection and analysis were performed by Zhonglan Qian. The first draft of the manuscript was written by Zhonglan Qian and all authors commented on previous versions of the manuscript. Critical revision was performed by Weichao Lyu and Yizhan Dai. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Jing Xu.

Ethics declarations

Competing Interests

The authors have no relevant financial or non-financial interests to disclose.

Ethics Approval

Not applicable.

Consent to Participate

Not applicable.

Consent for Publication

Not applicable.

Additional information

Publisher’s Note

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

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Qian, Z., Lyu, W., Dai, Y. et al. A Consensus-Based Model Predictive Control with Optimized Line-of-Sight Guidance for Formation Trajectory Tracking of Autonomous Underwater Vehicles. J Intell Robot Syst 106, 15 (2022). https://doi.org/10.1007/s10846-022-01710-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10846-022-01710-4

Keywords

Search

Navigation