An Optimization of Orbital Transfer for Spacecrafts with Finite-thrust Based on Legendre Pseudospectral Method
This paper presents the use of Legendre pseudospectral
method for the optimization of finite-thrust orbital transfer for
spacecrafts. In order to get an accurate solution, the System-s
dynamics equations were normalized through a dimensionless method.
The Legendre pseudospectral method is based on interpolating
functions on Legendre-Gauss-Lobatto (LGL) quadrature nodes. This
is used to transform the optimal control problem into a constrained
parameter optimization problem. The developed novel optimization
algorithm can be used to solve similar optimization problems of
spacecraft finite-thrust orbital transfer. The results of a numerical
simulation verified the validity of the proposed optimization method.
The simulation results reveal that pseudospectral optimization method
is a promising method for real-time trajectory optimization and
provides good accuracy and fast convergence.
 Qibo Peng "Finite-Thrust Trajectory Optimization Using a
Combinationof Gauss Pseudospectral Method and Genetic Algorithm".
(Chapter 4 of Genetic Algorithms in Applications Edited by Rustem
Popa, ISBN 978-953-51-0400-1, hard cover, 328 pages, Publisher: In
Tech, Published: March 21, 2012 under CC BY 3.0 license, in
subject Artificial Intelligence DOI: 10.5772/2675.
 Q. Gong, W. Kang and I. M. Ross, A Pseudospectral Method for The
Optimal Control of Constrained Feedback Linearizable Systems, IEEE
Trans. Auto. Cont., Vol.~51, No.~7, July 2006, pp.~1115-1129.
 J. S. Hesthaven, S. Gottlieb and D. Gottlieb, Spectral methods for
time-dependent problems, Cambridge University Press, 2007. ISBN
 Q. Gong, I. M. Ross, W. Kang and Fahroo, F., Connections between the
covector mapping theorem and convergence of pseudospectral methods
for optimal control, Computational Optimization and Applications,
Springer Netherlands, published online: 31 October 2007, to appear in