Design And Control Of Low-Energy Transfer Orbit In The Earth-Moon Three-Body System

With the rapid development of space science and technology,human enthusiasm for space exploration is unprecedented.As the natural satellite of the earth,the moon becomes the primary target of space exploration because of its unique geographical advantages.Economy is one of the main factors restricting the large-scale exploration and exploitation of the moon,today the important task of lunar exploration is to save as much energy as possible in the flight process of the probe.In recent years,with the gradual development and upgrading of lunar exploration activities around the world,how to use as little fuel as possible to achieve the transfer of the earth to the moon has become a research hotspot.This can not only greatly reduce the take-off weight of aircraft,greatly reduce the cost of space exploration,but also can carry out more space missions,improve the efficiency of the detector.Compared with the traditional Holman transfer in the two-body model,the Earth-Moon transfer method in the three-body model uses the gravity of third body instead of overcoming it.The obtained transfer orbit is closer to the real mechanical environment in space.Because of the low energy consumption in the whole transfer process,this kind of orbit is usually called Earth-Moon low-energy transfer orbit.There are three typical motion forms in the three-body problem:periodic orbit,chaotic motion and invariant manifold.These three forms of motion have their own characteristics.Based on the analysis of their respective characteristics,the design and control of transfer trajectories are carried out.The main research contents of this paper are as follows:(1)For periodic orbits,a fast calculation method for the circular restricted three-body problem is designed,and the results are extended to the elliptic restricted three-body problem by homotopy method.(2)For chaotic motion,in order to reduce the gliding time of the detector in the chaotic region,based on two ideas-cutting recurrent loops and tree of paths,the corresponding Earth-Moon transfer method are proposed respectively.(3)For invariant manifolds,a method of Earth-Moon transfer based on invariant manifolds of Lyapunov orbit about L₁ is designed to balance energy consumption and flight time.The main innovations of this paper are as follows:(1)A modified Poincarémap is created,on which projection points from every initial point are plotted.Compared with the traditional Poincarémap,evolution and fork of periodic orbits by initial point could be intuitively reflected,the corresponding relationship between the initial point and the projection point of the orbit could be clearly reflected,and the projection point could be marked on one modified Poincarémap when the orbit cross upward or downward the x axis.The numerical solution of periodic orbits with a given number of projections can be obtained through only a few iterations on the modified Poincarémap.(2)Based on the idea of cutting recurrent loops,a method of Earth-Moon transfer based on chaotic control about the structure of KAM(Kolmogorov-Arnold-Moser)toris is proposed.By dividing the structure of KAM toris in Poincarémap,the shortest transfer path is planned,which solves the shortcomings of blind searching in chaotic region.The final obtained Earth-Moon transfer orbit has advantages in comprehensive total energy consumption,transfer time and pulse number.(3)Based on the idea of the tree of paths,a chaotic multi-step control method for Earth-Moon transfer orbit is designed.Because of a chaotic orbits can spread over the whole chaotic region in the form of the tree,a disturbance in a given range are applied to the initial points of the orbits,then the Earth-Moon transfer orbit is finished by successive optimization.This method takes the arrival of orbit near the moon as the termination condition,so it does not need to preset the number of impulses needed in the transfer process.The transfer orbits with different flight time can be obtained by setting the disturbance range.(4)A hybrid method based on invariant manifold and chaos control is proposed.The transit orbits inside the invariant manifold tubes associated with the libration point L₁ is regarded as temporary regular chaotic trajectories,and the Earth-Moon transfer is finished by patching a transit orbit and a chaotic trajectory.This method take advantage of the sensitivity of chaos control to the initial state and the regularity of the invariant tube,the trade-off between energy consumption and flight time is realized.