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An Online Trajectory‐Planning Guidance Method for Reentry Vehicles With Bézier Curve–Based Shaping Approach.

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Title: An Online Trajectory‐Planning Guidance Method for Reentry Vehicles With Bézier Curve–Based Shaping Approach.
Authors: Hu, Yudong1,2 (AUTHOR) huyudong@hit.edu.cn, Wang, Zhehao1 (AUTHOR), Gao, Changsheng1,2 (AUTHOR), Jing, Wuxing1,2 (AUTHOR), Hu, Junbo1 (AUTHOR), Han, Tuo (AUTHOR) hantuo@buaa.edu.cn
Source: International Journal of Aerospace Engineering. 3/21/2026, Vol. 2026, p1-13. 13p.
Subjects: Trajectory optimization, Parametric equations, Space vehicles, Aerodynamics, Optimization algorithms, Flight planning (Aeronautics), Real-time control
Abstract: To improve the real‐time capability and adaptability of online trajectory‐planning guidance for reentry vehicles, a guidance method based on a Bézier curve shaping approach is proposed. Leveraging the inherent boundary condition satisfaction and smoothness characteristics of Bézier curves, both longitudinal and lateral guidance are designed. For lateral guidance, after nondimensionalizing the dynamic model, the ground track of the vehicle is described by Bézier curves with the help of their ability to satisfy the terminal constraints to avoid integral operations inherently. The functions of heading angle, bank angle, and aerodynamic forces about the Bézier curve parameters are derived, and according to the prescribed boundary conditions, the number of Bézier curve parameters to be determined is further reduced. Thus, the lateral guidance problem is transformed into a planning problem with a limited number of Bézier curve parameters as control variables. For longitudinal guidance, leveraging a predesigned angle‐of‐attack profile, the longitudinal dynamics model taking the Bézier curve parameters characterizing the lateral motion as the control variable is derived. Considering multiple constraints, the reentry guidance problems are transformed into optimization problems with the Bézier curve parameters characterizing the lateral motion as the control variable. The above optimization problem is then solved efficiently employing optimization algorithms. The results of simulations demonstrate that the guidance method developed in this paper significantly enhances the guidance accuracy and real‐time performance, while enhancing the smoothness of the flight trajectory and control variables. [ABSTRACT FROM AUTHOR]
Copyright of International Journal of Aerospace Engineering is the property of Wiley-Blackwell 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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  Label: Title
  Group: Ti
  Data: An Online Trajectory‐Planning Guidance Method for Reentry Vehicles With Bézier Curve–Based Shaping Approach.
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  Data: <searchLink fieldCode="AR" term="%22Hu%2C+Yudong%22">Hu, Yudong</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> huyudong@hit.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Wang%2C+Zhehao%22">Wang, Zhehao</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Gao%2C+Changsheng%22">Gao, Changsheng</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Jing%2C+Wuxing%22">Jing, Wuxing</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Hu%2C+Junbo%22">Hu, Junbo</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Han%2C+Tuo%22">Han, Tuo</searchLink> (AUTHOR)<i> hantuo@buaa.edu.cn</i>
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  Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Aerospace+Engineering%22">International Journal of Aerospace Engineering</searchLink>. 3/21/2026, Vol. 2026, p1-13. 13p.
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  Data: <searchLink fieldCode="DE" term="%22Trajectory+optimization%22">Trajectory optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Parametric+equations%22">Parametric equations</searchLink><br /><searchLink fieldCode="DE" term="%22Space+vehicles%22">Space vehicles</searchLink><br /><searchLink fieldCode="DE" term="%22Aerodynamics%22">Aerodynamics</searchLink><br /><searchLink fieldCode="DE" term="%22Optimization+algorithms%22">Optimization algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Flight+planning+%28Aeronautics%29%22">Flight planning (Aeronautics)</searchLink><br /><searchLink fieldCode="DE" term="%22Real-time+control%22">Real-time control</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: To improve the real‐time capability and adaptability of online trajectory‐planning guidance for reentry vehicles, a guidance method based on a Bézier curve shaping approach is proposed. Leveraging the inherent boundary condition satisfaction and smoothness characteristics of Bézier curves, both longitudinal and lateral guidance are designed. For lateral guidance, after nondimensionalizing the dynamic model, the ground track of the vehicle is described by Bézier curves with the help of their ability to satisfy the terminal constraints to avoid integral operations inherently. The functions of heading angle, bank angle, and aerodynamic forces about the Bézier curve parameters are derived, and according to the prescribed boundary conditions, the number of Bézier curve parameters to be determined is further reduced. Thus, the lateral guidance problem is transformed into a planning problem with a limited number of Bézier curve parameters as control variables. For longitudinal guidance, leveraging a predesigned angle‐of‐attack profile, the longitudinal dynamics model taking the Bézier curve parameters characterizing the lateral motion as the control variable is derived. Considering multiple constraints, the reentry guidance problems are transformed into optimization problems with the Bézier curve parameters characterizing the lateral motion as the control variable. The above optimization problem is then solved efficiently employing optimization algorithms. The results of simulations demonstrate that the guidance method developed in this paper significantly enhances the guidance accuracy and real‐time performance, while enhancing the smoothness of the flight trajectory and control variables. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of International Journal of Aerospace Engineering is the property of Wiley-Blackwell 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: 10.1155/ijae/5548526
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      – Code: eng
        Text: English
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        PageCount: 13
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      – SubjectFull: Trajectory optimization
        Type: general
      – SubjectFull: Parametric equations
        Type: general
      – SubjectFull: Space vehicles
        Type: general
      – SubjectFull: Aerodynamics
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      – SubjectFull: Optimization algorithms
        Type: general
      – SubjectFull: Flight planning (Aeronautics)
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      – SubjectFull: Real-time control
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      – TitleFull: An Online Trajectory‐Planning Guidance Method for Reentry Vehicles With Bézier Curve–Based Shaping Approach.
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            NameFull: Hu, Yudong
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            NameFull: Wang, Zhehao
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              M: 03
              Text: 3/21/2026
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              Y: 2026
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