A Fast Midcourse Trajectory Optimization Method for Interceptors Based on the Bézier Curve

This paper proposes a fast midcourse trajectory optimization method by using the Bézier curve as a transcription scheme to represent the interceptor trajectories. First, the trajectory optimization problem is established with the constraints during midcourse guidance and the performance index of the...

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Vydáno v:Aerospace Ročník 12; číslo 10; s. 893
Hlavní autoři: Li, Jingqi, Zhang, Gang, Cui, Liang
Médium: Journal Article
Jazyk:angličtina
Vydáno: Basel MDPI AG 01.10.2025
Témata:
Aircraft
Bézier curve
Constraints
Curves
Interceptors
Mathematical analysis
Mathematical optimization
Methods
Midcourse guidance
Midcourse trajectories
Optimization
Performance indices
Quadratic programming
Sea level
Terminal velocity
Trajectory optimization
Velocity
China
ISSN:2226-4310, 2226-4310
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Abstract This paper proposes a fast midcourse trajectory optimization method by using the Bézier curve as a transcription scheme to represent the interceptor trajectories. First, the trajectory optimization problem is established with the constraints during midcourse guidance and the performance index of the terminal velocity. Then, the interceptor position coordinates are represented using Bézier functions, which directly satisfy the boundary constraints. Other state and control variables are also expressed as Bézier functions. Finally, the original trajectory optimization problem is transformed into optimizing the Bézier parameters, which can be obtained by sequential quadratic programming. Numerical examples verify the rapidity of the proposed method when compared with various traditional numerical optimization methods. In addition, the result of the proposed method can be used as a fast solution satisfying all the boundary and path constraints, and it can also be used as an initial guess for further optimizations.
AbstractList This paper proposes a fast midcourse trajectory optimization method by using the Bézier curve as a transcription scheme to represent the interceptor trajectories. First, the trajectory optimization problem is established with the constraints during midcourse guidance and the performance index of the terminal velocity. Then, the interceptor position coordinates are represented using Bézier functions, which directly satisfy the boundary constraints. Other state and control variables are also expressed as Bézier functions. Finally, the original trajectory optimization problem is transformed into optimizing the Bézier parameters, which can be obtained by sequential quadratic programming. Numerical examples verify the rapidity of the proposed method when compared with various traditional numerical optimization methods. In addition, the result of the proposed method can be used as a fast solution satisfying all the boundary and path constraints, and it can also be used as an initial guess for further optimizations.
Audience Academic
Author Zhang, Gang
Li, Jingqi
Cui, Liang
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SubjectTerms Aircraft
Bézier curve
Constraints
Curves
Interceptors
Mathematical analysis
Mathematical optimization
Methods
Midcourse guidance
Midcourse trajectories
Optimization
Performance indices
Quadratic programming
Sea level
Terminal velocity
Trajectory optimization
Velocity
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Title A Fast Midcourse Trajectory Optimization Method for Interceptors Based on the Bézier Curve
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