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.
[1] 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.
[2] http://en.wikipedia.org/wiki/Optimal_control
[3] http://en.wikipedia.org/wiki/Pseudospectral_optimal_control
[4] 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.
[5] J. S. Hesthaven, S. Gottlieb and D. Gottlieb, Spectral methods for
time-dependent problems, Cambridge University Press, 2007. ISBN
978-0-521-79211-0
[6] 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
Journal, 2008.
[1] 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.
[2] http://en.wikipedia.org/wiki/Optimal_control
[3] http://en.wikipedia.org/wiki/Pseudospectral_optimal_control
[4] 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.
[5] J. S. Hesthaven, S. Gottlieb and D. Gottlieb, Spectral methods for
time-dependent problems, Cambridge University Press, 2007. ISBN
978-0-521-79211-0
[6] 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
Journal, 2008.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:55402", author = "Yanan Yang and Zhigang Wang and Xiang Chen", title = "An Optimization of Orbital Transfer for Spacecrafts with Finite-thrust Based on Legendre Pseudospectral Method", abstract = "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.", keywords = "Finite-thrust, Orbital transfer, Legendre
pseudospectral method", volume = "6", number = "8", pages = "969-5", }