Skip to main content
Log in

Immersion and Invariance-Based Nonlinear Control Synthesis for Depth Position of an AUV: Tracking and Regulation

  • Research Article-Electrical Engineering
  • Published:
Arabian Journal for Science and Engineering Aims and scope Submit manuscript

Abstract

This paper addresses the tracking control problem associated with the diving motion system of a torpedo-like shape autonomous underwater vehicle (AUV). A decoupled and reduced-order three degrees-of-freedom (3-DOF) nonlinear model is employed to represent the dynamics of the diving motion system for depth position control. The control objective is to track the demanded depth position in the presence of uncertainties and disturbances. A control law based on the immersion and invariance (I &I) technique is synthesized to achieve the control objectives. The proposed control law effectively tracks a stable, lower-order target dynamic system immersed within a three-dimensional manifold. Additionally, the regulation problem is treated as a specialized case of tracking, with a known depth serving as the reference input to be regulated. The performance of the proposed control law is assessed through simulation studies that consider various scenarios. The simulation study evaluates the robustness of the proposed control law resilience against modelling uncertainties and underwater disturbances. The simulations utilize the MAYA AUV, incorporating experimentally validated diving motion parameters. The proposed control law’s quantitative analysis and computational performance show better performance against the benchmark controller.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

Data Availability

This manuscript comprehensively documented all data generated throughout this study.

References

  1. Zhou, J.; Huang, H.; Huang, S.H.; Si, Y.; Shi, K.; Quan, X.; Guo, C.; Chen, C.-W.; Wang, Z.; Wang, Y.; Wang, Z.; Cai, C.; Hu, R.; Rong, Z.; He, J.; Liu, M.; Chen, Y.: Auh, a new technology for ocean exploration. Engineering (2022). https://doi.org/10.1016/J.ENG.2022.09.007

    Article  Google Scholar 

  2. Sahoo, A.; Dwivedy, S.K.; Robi, P.S.: Advancements in the field of autonomous underwater vehicle. Ocean Eng. 181, 145–160 (2019). https://doi.org/10.1016/J.OCEANENG.2019.04.011

    Article  Google Scholar 

  3. Fossen, T.I.: Handbook of Marine Craft Hydrodynamics and Motion Control. Handbook of Marine Craft Hydrodynamics and Motion Control (2011). https://doi.org/10.1002/9781119994138

  4. Silvestre, C.; Pascoal, A.: Depth control of the infante auv using gain-scheduled reduced order output feedback. Control. Eng. Pract. 15, 883–895 (2007). https://doi.org/10.1016/J.CONENGPRAC.2006.05.005

    Article  Google Scholar 

  5. Dong, Z.; Wan, L.; Li, Y.; Liu, T.; Zhuang, J.; Zhang, G.: Point stabilization for an underactuated auv in the presence of ocean currents. Int. J. Adv. Rob. Syst. 12(7), 100 (2015). https://doi.org/10.5772/61037

    Article  Google Scholar 

  6. Liu, C.; Xiang, X.; Yang, L.; Li, J.; Yang, S.: A hierarchical disturbance rejection depth tracking control of underactuated auv with experimental verification. Ocean Eng. 264, 112458 (2022). https://doi.org/10.1016/J.OCEANENG.2022.112458

    Article  Google Scholar 

  7. Yan, Z.P.; Yu, H.M.; Hou, S.P.: Diving control of underactuated unmanned undersea vehicle using integral-fast terminal sliding mode control. J. Cent. South Univ. 23, 1085–1094 (2016). https://doi.org/10.1007/S11771-016-0358-7/METRICS

    Article  Google Scholar 

  8. Li, J.H.; Lee, P.M.: Design of an adaptive nonlinear controller for depth control of an autonomous underwater vehicle. Ocean Eng. 32, 2165–2181 (2005). https://doi.org/10.1016/J.OCEANENG.2005.02.012

    Article  Google Scholar 

  9. Lapierre, L.: Robust diving control of an auv. Ocean Eng. 36, 92–104 (2009). https://doi.org/10.1016/J.OCEANENG.2008.10.006

    Article  Google Scholar 

  10. Ma, Z.; Hu, J.; Feng, J.; Liu, A.: Diving adaptive position tracking control for underwater vehicles. IEEE Access 7, 24602–24610 (2019). https://doi.org/10.1109/ACCESS.2019.2900448

    Article  Google Scholar 

  11. Lakhekar, G.V.; Waghmare, L.M.; Vaidyanathan, S.: Diving autopilot design for underwater vehicles using an adaptive neuro-fuzzy sliding mode controller. Stud. Comput. Intell. 635, 477–503 (2016). https://doi.org/10.1007/978-3-319-30169-3-21

    Article  Google Scholar 

  12. Lakhekar, G.V.; Waghmare, P.G.J.; Roy, R.G.: Robust diving motion control of an autonomous underwater vehicle using adaptive neuro-fuzzy sliding mode technique. IEEE Access 8, 109891–109904 (2020). https://doi.org/10.1109/ACCESS.2020.3001631

    Article  Google Scholar 

  13. Lei, M.: Nonlinear diving stability and control for an auv via singular perturbation. Ocean Eng. 197, 106824 (2020). https://doi.org/10.1016/J.OCEANENG.2019.106824

    Article  Google Scholar 

  14. Lin, Y.H.; Yu, C.M.; Wu, I.C.; Wu, C.Y.: The depth-keeping performance of autonomous underwater vehicle advancing in waves integrating the diving control system with the adaptive fuzzy controller. Ocean Eng. 268, 113609 (2023). https://doi.org/10.1016/J.OCEANENG.2022.113609

    Article  Google Scholar 

  15. Mahapatra, S.; Subudhi, B.: Nonlinear \(h_{\infty }\) state and output feedback control schemes for an autonomous underwater vehicle in the dive plane. Trans. Inst. Meas. Control. 40, 2024–2038 (2017). https://doi.org/10.1177/0142331217695671

    Article  Google Scholar 

  16. Qi, Y.; Wu, X.; Zhang, G.; Sun, Y.: Energy-saving depth control of an autonomous underwater vehicle using an event-triggered sliding mode controller. J. Mar. Sci. Eng. 10, 1888 (2022). https://doi.org/10.3390/JMSE10121888

    Article  Google Scholar 

  17. Tran, H.N.; Nhut Pham, T.N.; Choi, S.H.: Robust depth control of a hybrid autonomous underwater vehicle with propeller torque’s effect and model uncertainty. Ocean Eng. 220, 108257 (2021). https://doi.org/10.1016/j.oceaneng.2020.108257

    Article  Google Scholar 

  18. Wang, T.; Wu, C.; Wang, J.; Ge, T.: Modeling and control of negative-buoyancy tri-tilt-rotor autonomous underwater vehicles based on immersion and invariance methodology. Appl. Sci. 8(7), 1150 (2018). https://doi.org/10.3390/app8071150

    Article  Google Scholar 

  19. Zhang, X.; Yao, S.; Xing, W.; Feng, Z.: Fuzzy event-triggered sliding mode depth control of unmanned underwater vehicles. Ocean Eng. 266, 112725 (2022). https://doi.org/10.1016/J.OCEANENG.2022.112725

    Article  Google Scholar 

  20. Zhong, Y.; Yu, C.; Wang, R.; Liu, C.; Lian, L.: Adaptive depth tracking of underwater vehicles considering actuator saturation: theory, simulation and experiment. Ocean Eng. 265, 112517 (2022). https://doi.org/10.1016/J.OCEANENG.2022.112517

    Article  Google Scholar 

  21. Maurya, P.; Desa, E.; Pascoal, A.; Barros, E.; Navelkar, G.; Madhan, R.; Mascarenhas, A.; Prabhudesai, S.; Afzulpurkar, S.; Gouveia, A.; Naroji, S.; Sebastiao, L.: Control of the maya auv in the vertical and horizontal planes: theory and practical results. In: Proceedings of the 7th IFAC Conference on Manoeuvring and Control of Marine Craft, pp. 20–22 (2006)

  22. Tran, N.-H.; Choi, H.-S.; Nguyen, N.-D.; Jo, S.-W.; Kim, J.-Y.: Steering and diving control of a small-sized auv. In: AETA 2015: Recent Advances in Electrical Engineering and Related Sciences, pp. 619–632 (2016). Springer

  23. Nerkar, S.; Londhe, P.; Patre, B.: Design of super twisting disturbance observer based control for autonomous underwater vehicle. Int. J. Dyn. Control 10(1), 306–322 (2022)

    Article  Google Scholar 

  24. Londhe, P.; Dhadekar, D.D.; Patre, B.; Waghmare, L.: Uncertainty and disturbance estimator based sliding mode control of an autonomous underwater vehicle. Int. J. Dyn. Control 5, 1122–1138 (2017)

    Article  MathSciNet  Google Scholar 

  25. Hong, E.Y.; Soon, H.G.; Chitre, M.: Depth control of an autonomous underwater vehicle, starfish. In: OCEANS’10 IEEE SYDNEY, pp. 1–6 (2010). IEEE

  26. Yahya, M.; Arshad, M.; Majid, M.: Responsive surging, heading and diving controls of autonomous underwater vehicle based on brute forcing and smoothing of controllers. Indian J. Geo-Mar. Sci. 50(11), 884–889 (2022)

    Google Scholar 

  27. Sarif, N.M.; Ngadengon, R.; Abdul Kadir, H.; A Jalil, M.H.: Depth control of autonomous underwater vehicle using discrete time sliding mode controller. Univ. J. Electr. Electron. Eng. 6(5B), 96–102 (2019)

    Article  Google Scholar 

  28. Vahid, S.; Javanmard, K.: Modeling and control of autonomous underwater vehicle (auv) in heading and depth attitude via ppd controller with state feedback. Int. J. Coast. Offshore Environ. Eng. 1(4), 11–18 (2016)

    Google Scholar 

  29. Mostafa, S.; Elhalwagy, Y.; AboZied, M.; Kamel, A.: Control system design for steering and depth subsystems of autonomous underwater vehicle. J. Phys. Conf. Ser. 1721, 012031 (2021)

    Article  Google Scholar 

  30. Riaz, U.; Tayyeb, M.; Amin, A.A.: A review of sliding mode control with the perspective of utilization in fault tolerant control. Recent Adv. Electr. Electron. Eng. 14(3), 312–324 (2021)

    Google Scholar 

  31. Astolfi, A.; Ortega, R.: Immersion and invariance: a new tool for stabilization and adaptive control of nonlinear systems. IEEE Trans. Autom. Control 48, 590–606 (2003). https://doi.org/10.1109/TAC.2003.809820

    Article  MathSciNet  Google Scholar 

  32. Wang, L.; Forni, F.; Ortega, R.; Su, H.: Immersion and Invariance Stabilization of Nonlinear Systems: A Horizontal Contraction Approach, pp. 3093–3097. IEEE (2015)

    Google Scholar 

  33. Astolfi, A.; Karagiannis, D.; Ortega, R.: Nonlinear and adaptive control with applications (2008). https://doi.org/10.1007/978-1-84800-066-7

  34. Shao, X.; Liu, H.; Zhang, W.; Zhao, J.; Zhang, Q.: Path driven formation-containment control of multiple uavs: a path-following framework. Aerosp. Sci. Technol. 135, 108168 (2023). https://doi.org/10.1016/j.ast.2023.108168

    Article  Google Scholar 

  35. Manjarekar, N.S.; Banavar, R.N.; Ortega, R.: Stabilization of a synchronous generator with a controllable series capacitor via immersion and invariance. Int. J. Robust Nonlinear Control 22(8), 858–874 (2012). https://doi.org/10.1002/rnc.1732

  36. Lou, Z.E.; Zhao, J.: Viable immersion and invariance control for a class of nonlinear systems and its application to aero-engines. J. Franklin Inst. 356, 42–57 (2019). https://doi.org/10.1016/J.JFRANKLIN.2018.10.002

    Article  MathSciNet  Google Scholar 

  37. SNAME.: Nomenclature for treating the motion of a submerged body through a fluid: report of the American towing tank conference (1950)

  38. Prestero, T.T.J.: Verification of a six-degree of freedom simulation model for the remus autonomous underwater vehicle. PhD thesis, Massachusetts Institute of Technology (2001)

  39. Jalving, B.: The ndre-auv flight control system. IEEE J. Ocean. Eng. 19(4), 497–501 (1994). https://doi.org/10.1109/48.338385

    Article  Google Scholar 

  40. Maurya, P.; Morishita, H.M.; Aguiar, A.P.: A path-following controller for marine vehicles using a two-scale inner–outer loop approach. Sensors 22, 4293 (2022). https://doi.org/10.3390/S22114293

    Article  Google Scholar 

  41. Shtessel, Y.; Edwards, C.; Fridman, L.; Levant, A.: Sliding Mode Control and Observation. vol. 10 (1991)

  42. Sahu, B.K.; Subudhi, B.; Gupta, M.M.: Stability analysis of an underactuated autonomous underwater vehicle using extended-Routh’s stability method. Int. J. Autom. Comput. 15(3), 299–309 (2018)

  43. Song, K.-Y.; Behzadfar, M.; Zhang, W.-J.: A dynamic pole motion approach for control of nonlinear hybrid soft legs: a preliminary study. Machines 10(10), 875 (2022)

    Article  Google Scholar 

  44. Behbahani-Nejad, M.; Bagheri, A.: The accuracy and efficiency of a matlab-simulink library for transient flow simulation of gas pipelines and networks. J. Petrol. Sci. Eng. 70(3–4), 256–265 (2010)

    Article  Google Scholar 

  45. Lakhekar, G.; Waghmare, L.: Robust self-organising fuzzy sliding mode-based path-following control for autonomous underwater vehicles. J. Mar. Eng. Technol. 22(3), 131–152 (2023)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ravishankar P. Desai.

Ethics declarations

Conflict of interest

The authors affirm that they have no conflicts of interest to disclose.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) 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

Desai, R.P., Manjarekar, N.S. Immersion and Invariance-Based Nonlinear Control Synthesis for Depth Position of an AUV: Tracking and Regulation. Arab J Sci Eng (2024). https://doi.org/10.1007/s13369-024-08915-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s13369-024-08915-9

Keywords

Navigation