| With the increasing complexity of space missions,it’s becoming increasingly difficult for single satellites to meet the requirements of certain tasks,thus making satellite constellations consist of a number of satellites through certain configurations being widely used in the field of aerospace in recent years.However,if one of the constellation satellite has a damage or a failure,it will directly affect the function of the whole constellation.Therefore,the research of constellation traversal for the need of satellite maintenance attracts more and more attention.In this paper,the fuel optimal orbital design of a single spacecraft traversing a constellation using finite thrust model was proposed,and the widely used GPS constellation was used as a research object,where the correctness of the theory and constellation traversal orbits were simulated and verified by MATLAB and Satellite Tool Kit(STK).First of all,in order to find the transfer orbit with optimal fuel consumption,by using the ideal and simple method-impulse transfer mode,the preliminary exploration was carried out.Under the constraint of both fuel and time and by using the phase difference between constellation satellites,the optimal orbital transfer method-backward phase modulation orbital transfer method was proposed,where fuel consumption is inversely proportional to time consumption.The optimal GPS constellation traversal orbit design in two-body problem was then given using the proposed orbital transfer strategy and the configuration of the GPS satellite constellation.The correctness of the proposed theory was validated through STK simulation,which provided the initial idea and model for the study of the subsequent constellation traversal orbits design.Subsequently,due to the fact that impulse orbital transfer is too ideal and too difficult to achieve in practical engineering applications,while finite thrust is in line with the characteristics of the currently widely used engine,which makes using finite thrust to achieve the proposed backward phase modulation strategy more applicable in real engineering environment.Based on the least squares method,genetic algorithm and Gaussian pseudo-spectral method,the guidance laws that could satisfy the optimal fuel constraint in both coplanar and non-coplanar situations were given respectively.Through the analysis of the advantages and disadvantages of these three methods,a suitable combination guidance method for two-body problem was proposed in which the genetic algorithm was used to give initial values of control parameters to Gaussian pseudo-spectral method,and this finite thrust guidance law has high accuracy and computational efficiency.The optimal fuel orbit design scheme of GPS satellite constellation traversal based on finite thrust in two-body situation used this combined guidance law to calculate the initial and terminal states of each finite thrust orbit,and the simulation results of STK proved the feasibility of this theory.Finally,because the spacecraft’s orbit will be deviated from the two-body orbit by the effect of perturbations in space,by using the analytical solution of the kinetic equation of the spacecraft under the 2J perturbation given by the average elements method,the orbit of the target satellite could be calculated in advance,so as to facilitate the advance determination of the start and the terminal position during an orbital transfer which satisfy certain constraints.In the case of perturbation,the convergence of the genetic algorithm is poor,and the accuracy of the least squares method is lower than that of the Gaussian pseudo-spectral method.Therefore,only the Gaussian pseudo-spectral method was used to calculate the parameters of finite thrust orbital transfers and the appropriate orbit correction calculations that satisfy the optimal fuel constraint.The optimal orbit design scheme of GPS satellite constellation traversal based on finite thrust under 2J perturbation was proposed and verified by MATLAB calculation. |
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