Low-Thrust Out-of-Plane Orbital Station-Keeping Maneuvers for Satellites

This paper considers the problem of out of plane orbital maneuvers for station keeping of satellites. The main idea is to consider that a satellite is in an orbit around the Earth and that it has its orbit is disturbed by one or more forces. Then, it is necessary to perform a small amplitude orbital correction to return the satellite to its original orbit, to keep it performing its mission. A low thrust propulsion is used to complete this task. It is important to search for solutions that minimize the fuel consumption to increase the lifetime of the satellite. To solve this problem a hybrid optimal control approach is used. The accuracy of the satisfaction of the constraints is considered, in order to try to decrease the fuel expenditure by taking advantage of this freedom. This type of problem presents numerical difficulties and it is necessary to adjust parameters, as well as details of the algorithm, to get convergence. In this versions of the algorithm that works well for planar maneuvers are usually not adequate for the out of plane orbital corrections. In order to illustrate the method, some numerical results are presented.

[1]  Optimum Orbital Transfer by Impulses , 1960 .

[2]  Helio Koiti Kuga,et al.  Single frequency GPS measurements in real-time artificial satellite , 2003 .

[3]  Arthur E. Bryson,et al.  Applied Optimal Control , 1969 .

[4]  V. M. Gomes,et al.  A study of the close approach between a planet and a cloud of particles , 2009 .

[5]  D. J. Jezewski,et al.  An efficient method for calculating optimal free-space n-impulse trajectories. , 1968 .

[6]  Atair Rios Neto,et al.  A stochastic approach to the problem of spacecraft optimal manoeuvres , 1990 .

[7]  Helio Koiti Kuga,et al.  Orbital maneuvers using low-thrust , 2009 .

[8]  Karl G. Eckel,et al.  Optimal impulsive transfer with time constraint , 1982 .

[9]  THE FUNDAMENTAL GROUP OF TWO SPACES WITH A COMMON POINT , 1954 .

[10]  A. Prado.  Numerical Study and Analytic Estimation of Forces Acting in Ballistic Gravitational Capture , 2002 .

[11]  A. Prado,et al.  Constant Tangential Low-Thrust Trajectories near an Oblate Planet , 2001 .

[12]  R. Broucke,et al.  Transfer orbits in restricted problem , 1995 .

[13]  H. Mendlowitz,et al.  Soviet Space Science , 1959 .

[14]  A. Prado.  Numerical and analytical study of the gravitational capture in the bicircular problem , 2005 .

[15]  SUBOPTIMAL ANO HYBRIO NUMERICAL SOLUTION SCHEMES FOR ORBIT TRANSFER MANEUVERS , 1994 .

[16]  D. F. Lawden.  Minimal Rocket Trajectories , 1953 .

[17]  A. Prado.  Third-Body Perturbation in Orbits Around Natural Satellites , 2003 .

[18]  D. Jezewski,et al.  An analytic approach to two-fixed-impulse transfers between Keplerian orbits , 1982 .