Symbolic computation-based robust multistage NMPC for 3-D trajectory tracking of a ROV.

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Title: Symbolic computation-based robust multistage NMPC for 3-D trajectory tracking of a ROV.
Authors: Jiang, Xiaoyong1,2 (AUTHOR) 119082@zust.edu.cn, Yang, Zhenhai1 (AUTHOR), Wu, Yuxi1 (AUTHOR), Zhu, Qiyao1 (AUTHOR), Xu, Shutian1,3 (AUTHOR)
Source: Journal of Marine Science & Technology. Jun2025, Vol. 30 Issue 2, p295-310. 16p.
Subjects: Symbolic computation, Hessian matrices, Jacobian matrices, Ecological disturbances, Sensitivity analysis
Abstract: This paper presents a novel approach to solve the 3-D trajectory tracking problem for a remotely operated vehicle (ROV) using robust multistage nonlinear model predictive control (multistage NMPC) with symbolic computation. The proposed multistage control structure enhances the robustness of NMPC and improves control performance under environmental disturbances. The validity and robustness of the multistage NMPC approach are demonstrated through simulations conducted on a commercial-scale ROV operating under disturbances. Results show that the multistage NMPC approach outperforms the standard NMPC method and impressively is almost as good as the perfect information NMPC in solving the 3-D trajectory tracking problem for a ROV. Symbolic computation is employed to facilitate the implementation of the multistage NMPC approach. Specifically, symbolic computation is used to obtain the Jacobian and Hessian matrices required for the multistage NMPC method. The sensitivity analysis on the terminal cost shows that an appropriate terminal cost enhances the multistage NMPC controller performance, allowing for shorter prediction horizons without compromising accuracy. Simulations reveal that higher-frequency disturbances are easier to "average out" for both standard and multistage NMPC. Yet, the multistage NMPC approach yields much better accuracy across all tested frequencies. The simulations demonstrate that the proposed multistage NMPC approach can be solved for the 3-D trajectory tracking problem in real time. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Marine Science & Technology is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Symbolic computation-based robust multistage NMPC for 3-D trajectory tracking of a ROV.
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  Data: <searchLink fieldCode="AR" term="%22Jiang%2C+Xiaoyong%22">Jiang, Xiaoyong</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> 119082@zust.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Yang%2C+Zhenhai%22">Yang, Zhenhai</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Wu%2C+Yuxi%22">Wu, Yuxi</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Zhu%2C+Qiyao%22">Zhu, Qiyao</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Xu%2C+Shutian%22">Xu, Shutian</searchLink><relatesTo>1,3</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Marine+Science+%26+Technology%22">Journal of Marine Science & Technology</searchLink>. Jun2025, Vol. 30 Issue 2, p295-310. 16p.
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  Data: <searchLink fieldCode="DE" term="%22Symbolic+computation%22">Symbolic computation</searchLink><br /><searchLink fieldCode="DE" term="%22Hessian+matrices%22">Hessian matrices</searchLink><br /><searchLink fieldCode="DE" term="%22Jacobian+matrices%22">Jacobian matrices</searchLink><br /><searchLink fieldCode="DE" term="%22Ecological+disturbances%22">Ecological disturbances</searchLink><br /><searchLink fieldCode="DE" term="%22Sensitivity+analysis%22">Sensitivity analysis</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: This paper presents a novel approach to solve the 3-D trajectory tracking problem for a remotely operated vehicle (ROV) using robust multistage nonlinear model predictive control (multistage NMPC) with symbolic computation. The proposed multistage control structure enhances the robustness of NMPC and improves control performance under environmental disturbances. The validity and robustness of the multistage NMPC approach are demonstrated through simulations conducted on a commercial-scale ROV operating under disturbances. Results show that the multistage NMPC approach outperforms the standard NMPC method and impressively is almost as good as the perfect information NMPC in solving the 3-D trajectory tracking problem for a ROV. Symbolic computation is employed to facilitate the implementation of the multistage NMPC approach. Specifically, symbolic computation is used to obtain the Jacobian and Hessian matrices required for the multistage NMPC method. The sensitivity analysis on the terminal cost shows that an appropriate terminal cost enhances the multistage NMPC controller performance, allowing for shorter prediction horizons without compromising accuracy. Simulations reveal that higher-frequency disturbances are easier to "average out" for both standard and multistage NMPC. Yet, the multistage NMPC approach yields much better accuracy across all tested frequencies. The simulations demonstrate that the proposed multistage NMPC approach can be solved for the 3-D trajectory tracking problem in real time. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Marine Science & Technology is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s00773-025-01051-5
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      – Code: eng
        Text: English
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        PageCount: 16
        StartPage: 295
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      – SubjectFull: Symbolic computation
        Type: general
      – SubjectFull: Hessian matrices
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      – SubjectFull: Jacobian matrices
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      – SubjectFull: Ecological disturbances
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      – SubjectFull: Sensitivity analysis
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      – TitleFull: Symbolic computation-based robust multistage NMPC for 3-D trajectory tracking of a ROV.
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            NameFull: Jiang, Xiaoyong
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            NameFull: Yang, Zhenhai
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            NameFull: Wu, Yuxi
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            NameFull: Zhu, Qiyao
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            – D: 01
              M: 06
              Text: Jun2025
              Type: published
              Y: 2025
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