Analytic solution to optimal reconfigurations of satellite formation flying in circular orbit under J2 perturbation

Hancheol Cho, Sang Young Park, Han Earl Park, Kyu Hong Choi

Research output: Contribution to journalArticle

10 Citations (Scopus)


This paper presents an analytic solution to the optimal reconfiguration problem of satellite formation flying in $J-2$ orbital perturbation. Continuous and variable low-thrust accelerations are represented by the Fourier series, and initial and final boundary conditions are used to establish the constraints on the thrust functions. The thrust functions are implemented by optimal Fourier coefficients that minimize the cost during the maneuver. The analytic solution composed of these Fourier coefficients are simply represented in a closed form, and no approximation is needed. Numerical simulations are conducted to visualize and compare the results obtained in this paper with those of previous papers with no perturbations. The analytic solution developed in this paper is more accurate in that the general behavior of the optimal control history and reconfiguration trajectories are easily calculated even in the presence of the $J-2$ potential disturbance. The analytic solution is useful for designing a reconfiguration controller for satellite formation flying under $J-2$ orbital perturbation.

Original languageEnglish
Article number6237587
Pages (from-to)2180-2197
Number of pages18
JournalIEEE Transactions on Aerospace and Electronic Systems
Issue number3
Publication statusPublished - 2012 Jul 23


All Science Journal Classification (ASJC) codes

  • Aerospace Engineering
  • Electrical and Electronic Engineering

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