A new control law based on characteristic exponent assignment for libration point orbit maintenance

A new method is developed for stabilizing motion on collinear libration point orbits using the formalism of the circular restricted three body problem. Linearization about the collinear libration point orbits yields an unstable linear parameter-varying system with periodic coefficients. Given the variational equations, an innovative control law based on characteristic exponent assignment is introduced for libration point orbit maintenance. A numerical simulation choosing the Richardson＇s third order approximation for a halo orbit as a nominal orbit is conducted, and the results demonstrate the effectiveness of this control law.

Trajectory correction for lunar flyby transfers to libration point orbits using continuous thrust

Trajectory corrections for lunar flyby transfers to Sun–Earth/Moon libration point orbits(LPOs)with continuous thrusts are investigated using an ephemeris model.The lunar flyby transfer has special geometrical and dynamical structures;therefore,its trajectory correction strategy is considerably different from that of previous studies and should be specifically designed.In this paper,we first propose a control strategy based on the backstepping technique with a dead-band scheme using an ephemeris model.The initial error caused by the launch time error is considered.Since the perturbed transfers significantly diverge from the reference transfers after the spacecraft passes by the Moon,we adopt two sets of control parameters in two portions before and after the lunar flyby,respectively.Subsequently,practical constraints owing to the navigation and propellant systems are introduced in the dynamical model of the trajectory correction.Using a prograde type 2 orbit as an example,numerical simulations show that our control strategy can efficiently address trajectory corrections for lunar flyby transfers with different practical constraints.In addition,we analyze the effects of the navigation intervals and dead-band scheme on trajectory corrections.Finally,trajectory corrections for different lunar flyby transfers are depicted and compared.

Quasi-periodic orbits of small solar sails with time-varying attitude around Earth–Moon libration points

This paper proposes new quasi-periodic orbits around Earth–Moon collinear libration points using solar sails.By including the time-varying sail orientation in the linearized equations of motion for the circular restricted three-body problem(CR3BP),four types of quasi-periodic orbits(two types around L1 and two types around L2)were formulated.Among them,one type of orbit around L2 realizes a considerably small geometry variation while ensuring visibility from the Earth if(and only if)the sail acceleration due to solar radiation pressure is approximately of a certain magnitude,which is much smaller than that assumed in several previous studies.This means that only small solar sails can remain in the vicinity of L2 for a long time without propellant consumption.The orbits designed in the linearized CR3BP can be translated into nonlinear CR3BP and high-fidelity ephemeris models without losing geometrical characteristics.In this study,new quasi-periodic orbits are formulated,and their characteristics are discussed.Furthermore,their extendibility to higher-fidelity dynamic models was verified using numerical examples.

On the dynamics and control of the Sun-Earth L_(2) tetrahedral formation

The dynamics and control of a tetrahedral spacecraft formation flying in the Sun-Earth L2 region is initiatively studied,based on the circular restricted three-body problem(CR3BP).Driven by the science goal of identifying extra-solar terrestrial planets and the requirement of imaging optics,a conceptional four-spacecraft triangular pyramid configuration has been proposed for the Multiple-spacecraft Exoplanet Aperture sYnthetic INterferometer(MEAYIN)project,China’s first mid-infrared interferometric imaging mission.Although it looked promising from an optical perspective,the configuration has not been verified dynamically.The formation is required to be virtually“rigid”,because its mutual distances and inertial pointing direction must be maintained with very high accuracy during each observation.In this study,the spatial geometrical relationship between the four spacecraft was established by introducing the parameters of lengths,angles,and a reference vector.The first contribution is that a compact set of normalized factors and critical time indices are defined,which can provide a complete description of the drift of the shape and pointing direction of the configuration,caused by the unstable dynamical environment.Five design variables are isolated and analyzed,and their individual impacts on the uncontrolled evolution of the formation are studied.The main results obtained reveal that the dimensions of the rigid configuration allow a free drift for a time period on the order of tens of hours,while the inertial pointing direction will be lost within merely tens of seconds.Therefore,to form a rigid configuration,the control challenge lies in the fact that control efforts are frequently required for each spacecraft in the fleet,owing to the diverging dynamics.As a second contribution,a simple and feasible control algorithm is proposed to maintain the rigidity of the formation configuration.The results indicate that the associated energy cost is merely 0.05 m/s per observation on average.