Dynamics And Rendezvous Control Of The Earth-moon Libration Points

Libration points are the equilibria of the Circular Restricted Three-Body Problem(CR3BP). Owing to the unique dynamics, libration points have been among the most frontier topics in both the celestial mechanics and the astrodynamics fields. With the success of the extended mission of "CHANG’E-2" and the recent announcement of the "Kua Fu" project’s entrance into the construction stage, China has also entered an era of libration point applications. For future possible missions in this region, the dynamics and control of the collinear points in the real Earth-Moon system are studied in this thesis. The main work is as follows:Design of the transfer orbit from Earth parking orbits to libration point orbits. The first problem confronted in libration point application is how to arrive at the libration point orbits. In this work, the transfer problem from a LEO to an Earth-Moon L2 point halo orbit is studied. In the first place, a differential correction algorithm is given for obtaining a transfer arc approching the close proximity of the Moon and then patching to the stable manifold of the halo orbit with a second maneuver. The computation of the LEO departure delta-v is discussed in detail. Morever, with the aid of introducing several coordinate systems, the computational aspects of the LEO inclination is also analyzed.Dynamics of the collinear points in the real Earth-Moon system. CR3 BP is not an ideal model for the Earth-Moon system due to the strong perturbation of the Sun. The long-term dynamics of the collinear points has to be eventually analyzed in the n-body ephemeris model. In order to do this, an algorithm is proposed in the first place to obtain real libration point orbits lasting for over 60 years. It uses as initial guess only a short-term CR3 BP orbit and then generates longer trajectories by iteratively using multiple shooting and Fourier analysis. A number of applications of the proposed algorithm include the dynamical substitutes of the collinear libration points, the refinement of the periodic orbits(planar Lyapunov orbit, vertical Lyapunov orbit, and halo orbit), and the refinement of the quasi-periodic ones(Lissajous orbit and quasi-halo orbit). Poincaré maps are also given to show the dynamical structure of the central manifolds around the collinear points in both the CR3 BP model and the ephemeris one. In addition, it has been found that the frequencies of the refined orbits can be adjusted as simple linear combinations of the basic frequencies in the Earth-Moon system.Long-term stationkeeping of the real Earth-Moon libration point orbits. Collinear libration points are inherently unstable. A spacecraft will deviate from its nominal path at an exponential rate if no control attempt is made. Three "tight" control strategies, i.e., the ones closely following a nominal orbit, are proposed to be used for the long-term stationkeeping of the real Earth-Moon libration point orbits. These strategies are the discrete-time LQR, the target point method, and the discrete-time sliding mode control(DSMC). The simulation is done for 10 years, much longer than any implemented mission, in the full ephemeris model and practical constraints and various errors are also considered. By comparing with each other, the obtained results fully validate the efficiency of the target point method and the DSMC.Near-range libration point rendezvous guidance and control. With the rising needs for space services from future libration point missions, the Rendezvous and docking(RVD) problem should be studied in depth to adapt to the high nonlinearity and instability in the libration point region. Two control methods are proposed for the near-range rendezvous in this region. One is termed the time-fixed glideslope approach, which inherits the simplicity of the traditional method, and more importantly, overcomes the difficulty that the time of flight can not be fixed a priori. The other approach is the terminal sliding mode control augmented with PWPF thrust modulation. Extensive simulation is done with various errors taken into account. The performances of both methods are compared in detail.In summary, based on theoretical analysis and numerical simulation, the dynamics and control of the collinear points in real Earth-Moon system are studied in depth. The obtained results are to provide technical reference for future missions.