Rendezvous Trajectory Design And Error Analysis Of Libration Point Orbits

Libration points are force equilibrium points in the restricted three body problem,and they have unique spatial positions.There are many types of periodic orbits in the vicinity of libration points,which have important application values in deep space missions.Aiming at the construction of libration space station in the future,this dissertation studies the libration point rendezvous trajectory design and error propagation characteristics.The main research contents are as follows.The libration point rendezvous trajectory is designed based on three body Lambert algorithm and the classical three-body Lambert algorithm is improved.Due to the drawback of classical three-body Lambert algorithm,a method is proposed that the initial reference trajectory is first solved with genetic algorithm and then improved with homotopy Newton–Raphson method.The relationship between the rendezvous velocity increment and the initial phase difference for spacecraft on the same Halo orbit is analyzed both in Sun-Earth and Earth-Moon three-body systems.The relationship between the rendezvous velocity increment and the amplitude difference of Halo orbits for spacecraft on different Halo orbits is also analyzed.The velocity increment of rendezvous trajectory with relatively long time is computed both by classical three-body Lambert algorithm and the improved version,and the result validates the effectiveness of the improved algorithm.The error propagation characteristic of Halo orbit is analyzed using the condition number of monodromy matrix.It is demonstrated that the eigenvalues of the monodromy matrix of the different positions on the Halo orbit are the same,so the eigenvalue method cannot be used to estimate the error sensitivity of different positions on Halo orbit.The condition number of monodromy matrix is proposed to estimate the error sensitivity of different positions on a Halo orbit.Covariance propagation method and Monte Carlo simulation are applied to analyze the influence of the components of initial position and velocity errors on the termianl position and velocity.The condition number of monodromy matrix and standard deviations of the position errors are computed for the Halo orbits with different amplitudes and the Halo orbits in systems with different mass ratios,which demonstrates the validity of estimating the error sensitivity of different positions on Halo orbit by condition number.The variation trends of the condition numbers along propagation time corresponding to different points on the Halo orbit are analyzed,and the conclusion offers a criterion to help select the Halo orbit injection point with relatively low error sensitivity.The multi-objective optimization model for the multi-stage Halo orbit rendezvous mission is designed and preliminarily solved.The Halo orbit rendezvous mission is divided to the Earth-Halo transfer trajectory,the Halo station-keeping orbit and the Halo rendezvous trajectory.The single impulse Earth-Halo transfer trajectory is designed and its existential condition is analyzed.The two-impulse transfer trajectory is designed based on the least squares differential corrections method and the influence of Halo orbit injection point on the velocity increment and transfer time is also analyzed.The relative motion characteristics between the chaser and target spacecraft are analyzed for two situations that the station-keeping orbit is the same as the target orbit and is different from the target orbit.The same Halo orbit is selected as the station-keeping orbit.The time relative to the start epoch,waiting time on the staion-keeping orbit and the rendezvous trajectory transfer time are set as design parameters.The total mission time and velocity increment are set as the object functions,and then the multi-objective optimization model for the multi-stage Halo orbit rendezvous mission is built.The Pareto optimal set of the rendezvous tranectory is computed with the Nondominated Sorting Genetic Algorithm Ⅱ(NSGA-Ⅱ).This paper studies the three-body Lambert algorithm,the error propagation characteristics and the multi-stage rendezvous mission planning method of libration point rendezvous trajectory.The conclusions of this paper can provide a reference to the construction of the libration point space station of our country in the future.