The Study Of Satellites Formation Based On The Restricted Three Body Problem

With the development of technology and the progress of the world, the mysteries of universe has drawn human's interest. Since 1957, countries have been carrying out space race and eager to enter the field of Space quest. The development of satellite has gradually become a symbol of national strength. However, the satellite mass, volume and development costs, cycle cannot handle with the increase in mission requirements the small satellite formation technology came into being.Firstly, the developments in small satellite formation elaborated by the research projects at home and abroad has been descript; then the dynamics model has been descript in dynamics and kinematics respectively by relative dynamic; then the perturbations development are described near-Earth orbit and deep space exploration; and the restricted three-body environment has been studied mainly into circular restricted three-body and fully restricted three-body two aspects; Finally the techniques of controller applied to formation of satellite has been analyzed.Formation satellite mission is composed by the relative movements between some follower satellites and a main satellite. So the relationship between one follower and leader is the foundation of formation. This paper studies the two-body environment, while establishing relative motion dynamics model based on Hill equation. Then the restricted three-body environment of Earth/Moon-Sun has been analyzed and the environment strengths near Lagrange points. At last, the dynamics model is established and nonlinear term has been linearised.Near the 2L point of Earth/Moon-Sun, the gravitation of spacecraft is equal, so the control will be a leading role for the satellites trajectory. Comparing to traditional promoting, the solar sail control can achieve continuous, accurate thrust, easier to complete a formation task. This paper analyzes the solar sail pressure and the attitude angle. For the binary system, one of the astronomical cannot be sphere, so the potential function will be used to solve perturbation. Aiming at 1999KW4 binary system, simplified it's model, the formation dynamics model is built by ellipsoid potential function.A linear controller can be used to control the formation in Earth/Moon-Sun. This article designed a linear quadratic regulator based on the formations linearized model, taking into account the formation team, the energy consumption and control time to make three followers complete the task of configuration from circular team to the position of learder. While for the nonlinear dynamics model in binary system, we use a neural network controller to be reconstructed. HBF neural network is a generalization based radial basis function network, while using convex combination algorithm(CCA) to optimize the single hidden layer neural network enable it approximate complex nonlinear function in higher precision.In summary, this paper studied the restrict three problem of Earth/Moon-Sun and binary system, established the satellites formation dynamic model. according to the radiation solar pressure and perturbation to reconstruct formation; for the linear models, a LQR controller is designed and for the non-linear model, a HBF neural network controller based on CCAis used to complete the task.