Analytic solution for fuel-optimal reconfiguration in relative motion

H. C. Cho, Sang-Young Park

Research output: Contribution to journalArticle

32 Citations (Scopus)

Abstract

The current paper presents simple and general analytic solutions to the optimal reconfiguration of multiple satellites governed by a variety of linear dynamic equations. The calculus of variations is used to analytically find optimal trajectories and controls. Unlike what has been determined from previous research, the inverse of the fundamental matrix associated with the dynamic equations is not required for the general solution in the current study if a basic feature in the state equations is met. This feature is very common due to the fact that most relative motion equations are represented in the LVLH frame. The method suggested not only reduces the amount of calculations required, but also allows predicting the explicit form of optimal solutions in advance without having to solve the problem. It is illustrated that the optimal thrust vector is a function of the fundamental matrix of the given state equations, and other quantities, such as the cost function and the state vector during the reconfiguration, can be concisely represented as well. The analytic solutions developed in the current paper can be applied to most reconfiguration problems in linearized relative motions. Numerical simulations confirm the brevity and accuracy of the general analytic solutions developed in the current paper.

Original languageEnglish
Pages (from-to)495-512
Number of pages18
JournalJournal of Optimization Theory and Applications
Volume141
Issue number3
DOIs
Publication statusPublished - 2009 Jun 1

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Reconfiguration
Analytic Solution
Fundamental Matrix
State Equation
Dynamic Equation
Motion
Cost functions
Equations of motion
Optimal Trajectory
Trajectories
Satellites
Calculus of variations
General Solution
Cost Function
Linear equation
Computer simulation
Optimal Control
Optimal Solution
Numerical Simulation

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

Cite this

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Analytic solution for fuel-optimal reconfiguration in relative motion. / Cho, H. C.; Park, Sang-Young.

In: Journal of Optimization Theory and Applications, Vol. 141, No. 3, 01.06.2009, p. 495-512.

Research output: Contribution to journalArticle

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