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arXiv · 2506.13921

A Study on Effective Initial Guess Finding Method Based on Bézier Curves: Orbit Determination Applications

Daegyun Choi·Sungwook Yang·Henzeh Leeghim·Donghoon Kim
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Abstract

In celestial mechanics, proper orbits related to missions are obtained by solving two-point boundary value problems. Since a selection method of initial value affects the convergence of the solution, developing an effective method to find an initial guess is required. In this work, Bézier curves, which can describe complicated curves and surfaces, are utilized to find the initial guess. First, the given problems are transformed into Bézier curves forms, and Bézier curves' control points, which can handle the shape of curves, are selected by solving the system of nonlinear equations. Finally, the initial guess is obtained by substituting the calculated control points to Bézier curves. To validate the performance of the proposed method, numerical simulations are conducted with respect to three kinds of orbits, which are from circular to highly elliptical orbit (HEO). The proposed method is compared to the general shooting method. The comparison results show that the initial guess calculated by Bézier curves makes finding the solution more efficient in terms of computational time and iterations. Also, it shows that the proposed method finds the solution for the HEO while the general shooting method fails to find the solution.

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Daegyun Choi, Sungwook Yang, Henzeh Leeghim, Donghoon Kim. 2026-08-06. A Study on Effective Initial Guess Finding Method Based on Bézier Curves: Orbit Determination Applications. https://arxiv.org/abs/2506.13921

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