Orbital Evolution And Control For Long-term Bounded Lunar Nanosat Formation

Lunar and deep space exploration has become the focus of space activities in various countries.Different from the national space activities in the 1960s,modern deep space exploration demands low cost.Using nanosatellites,especially cube satellites,for deep space exploration has come into fashion.The analysis,design,and control of satellite orbit run through the space mission.The focus is on how to deal with perturbations.Unlike the Earth satellite,the C₂₂and J₂perturbation of the lunar satellite has the same magnitude,and the third-body perturbation is remarkable.As a consequence,the theory of the Earth satellite cannot be applied directly.Aiming at lunar formation flying,this thesis discusses the long-term evolution of orbits,the long-term boundedness condition for formation flying and formation control based on environmental force,for eliminating the perturbation effect and reducing fuel consumption.The research results have been obtained as follows:With more accurate of the orbital dynamics modeling,the designed orbit is closer to reality.Consequently,the fuel consumption for orbit maintenance is lower.Thus,a method based on von-Zeiepel theory is proposed for deriving the averaged dynamics and the explicit conversion between osculating elements and mean elements,considering J₂,C₂₂and third-body perturbations.This method uses von-Zeipel transform to construct a generating function for eliminating the mean anomaly of the satellite and the perturbating orbit.Afterwards,the explicit transformation between osculating elements and mean elements is obtained by differentiating the generating function,and the averaged dynamics is derived based on the averaged Hamiltonian function.These theories are applied to the design of lunar frozen orbits.Finally,the numerical simulation is conducted,and results show that the proposed transformation between osculating elements and mean elements is more accurate and the frozen orbit is more stable.Formation requires the relative positions between satellites within a bounded range.An algorithm is proposed to design long-term bounded lunar formation under complex perturbations from the point view of the averaged relative distance,which is calculated by averaging the osculating relative distance with respect to the mean anomalies of the satellite and the perturbating orbit.The analytical solution of the averaged distance is obtained under the assumption of the chief on a frozen orbit.The analytical invariant distance condition is derived based on this expression.Moreover,an optimization model is constructed to minimize the initial relative velocity and accelerations by weighting factors,and how to choose a weighting factor is discussed.The constraints of long-term bounded formation are obtained by solving the optimization model.Finally,the proposed theories are used to design bounded formation at low-and high-altitude orbits with frozen or non-frozen characteristics.The simulation results indicate that the invariant condition is more suitable for designing low-altitude formations with the chief on a frozen orbit,and the optimized boundedness constraints behave better in mitigating the increase of the averaged distance in all cases,compared with the constraints proposed by previous works.For further reducing the potential perturbation effects,it is a good choice to select high-altitude orbits for lunar formations,where the third-body perturbation is more than an order of magnitude higher than other perturbations.A general third-body perturbation,considering the eccentricity and inclination of the perturbating body’s orbit,is considered.The short-period effects of the general third-body perturbation are eliminated via averag-ing.Its long-term effects are analyzed based on series analysis and numerical simulation.It can be concluded that the differences between orbital eccentricity,inclination,and right ascension of the ascending node are the main factors responsible for large oscillations of the relative distance.Afterwards,the analytical boundedness condition for high-altitude lunar formation is derived by restraining these differential elements and long-term drifts of the single-averaged distance.Finally,the simulation results validate the effectiveness of the new boundedness condition.Using environmental forces for lunar formation keeping is an available way to reduce fuel consumptions.A formation controller based on differential solar radiation pressure（DSRP）is proposed,utilizing mean orbital element feedback,for regulating relative distances between satellites in lunar orbits.It is shown that the most effective way to mitigate the inter-satellite drift,is to adjust the semimajor axes.This is achieved by modifying the cross-sectional areas of the satellites.The stability of the closed-loop system is proven based on the finite-time stability theory.Numerical simulation results illustrate that the new DSRP-based controller is able to arrest the relative distance drift in lunar orbits for several years.