Minimum-time trajectory optimization of multiple revolution low-thrust Earth-orbit transfers

Kathryn F. Graham, Anil V. Rao, D. Spencer

Research output: Contribution to journalArticle

26 Citations (Scopus)

Abstract

The problem of determining high-accuracy minimum-time Earth-orbit transfers using low-thrust propulsion is considered. The optimal orbital transfer problem is posed as a constrained nonlinear optimal control problem and is solved using a variable-order Legendre-Gauss-Radau quadrature orthogonal collocation method. Initial guesses for the optimal control problem are obtained by solving a sequence of modified optimal control problems where the final true longitude is constrained and the mean square difference between the specified terminal boundary conditions and the computed terminal conditions is minimized. It is found that solutions to the minimumtime low-thrust optimal control problem are only locally optimal, in that the solution has essentially the same number of orbital revolutions as that of the initial guess. A search method is then devised that enables computation of solutions with an even lower cost where the final true longitude is constrained to be different from that obtained in the original locally optimal solution. A numerical optimization study is then performed to determine optimal trajectories and control inputs for a range of initial thrust accelerations and constant specific impulses. The key features of the solutions are then determined, and relationships are obtained between the optimal transfer time and the optimal final true longitude as a function of the initial thrust acceleration and specific impulse. Finally, a detailed postoptimality analysis is performed to verify the close proximity of the numerical solutions to the true optimal solution.

Original languageEnglish (US)
Pages (from-to)711-727
Number of pages17
JournalJournal of Spacecraft and Rockets
Volume52
Issue number3
DOIs
StatePublished - Jan 1 2015

Fingerprint

trajectory optimization
low thrust
Orbital transfer
Earth orbits
optimal control
thrust
longitude
Earth (planet)
trajectory
Trajectories
specific impulse
low thrust propulsion
transfer orbits
collocation
quadratures
proximity
impulses
boundary condition
Propulsion
trajectories

All Science Journal Classification (ASJC) codes

  • Aerospace Engineering
  • Space and Planetary Science

Cite this

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abstract = "The problem of determining high-accuracy minimum-time Earth-orbit transfers using low-thrust propulsion is considered. The optimal orbital transfer problem is posed as a constrained nonlinear optimal control problem and is solved using a variable-order Legendre-Gauss-Radau quadrature orthogonal collocation method. Initial guesses for the optimal control problem are obtained by solving a sequence of modified optimal control problems where the final true longitude is constrained and the mean square difference between the specified terminal boundary conditions and the computed terminal conditions is minimized. It is found that solutions to the minimumtime low-thrust optimal control problem are only locally optimal, in that the solution has essentially the same number of orbital revolutions as that of the initial guess. A search method is then devised that enables computation of solutions with an even lower cost where the final true longitude is constrained to be different from that obtained in the original locally optimal solution. A numerical optimization study is then performed to determine optimal trajectories and control inputs for a range of initial thrust accelerations and constant specific impulses. The key features of the solutions are then determined, and relationships are obtained between the optimal transfer time and the optimal final true longitude as a function of the initial thrust acceleration and specific impulse. Finally, a detailed postoptimality analysis is performed to verify the close proximity of the numerical solutions to the true optimal solution.",
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Minimum-time trajectory optimization of multiple revolution low-thrust Earth-orbit transfers. / Graham, Kathryn F.; Rao, Anil V.; Spencer, D.

In: Journal of Spacecraft and Rockets, Vol. 52, No. 3, 01.01.2015, p. 711-727.

Research output: Contribution to journalArticle

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