Study On Formation Design And Stationkeeping Of Spacecraft Formation Flying

In recent years, satellite formation flying has received much attention and became a hot topic in the space community because of the possible advantages of replacing a single, complex satellite with a cluster of smaller ones. Flying a formation of satellites offers improved flexibility and redundancy and the ability to construct much large virtual sensors than can be flown on a single monolithic satellite.In this background, the thesis concentrates on the study of the formation design and station keeping, one of the critical technologies of formation flying. There are two primary constraints in the formation design and station keeping. First is the mission constraint, that is, various formation flying missions' requirements for the formation arrays. Second is the orbit constraint, that is, the needs of searching the nature periodic relative motion orbits. The purpose of the formation design and station keeping is satisfying two constraints with the least propellant cost. The main work and achievements are summarized as follows:From the point of view of the formation satellites system energy, the vectorial form of the generalized relative dynamic equations is derived by the Lagrange method. Using the vectorial dynamic equations, the Cartesian forms of the dynamic equations considering the nonlinearity and the J₂ perturbations are presented respectively, which are the dynamic bases for the later study.Working with the energy matching principle, the algebraic method is presented to establish the periodic relative motion condition, that is, the orbit constraint for the formation designing and station keeping. The analytic expressions of the periodic relative motion condition considering nonlinearity and eccentricity are conveniently derived by the presented method. The reason causes the different precision between the dynamic method and the kinematical method is studied and the modified method is given to make the dynamic method have the same precision as the kinematical method.Utilizing the orbit constraint derived from the presented algebraic method, the innovational methodology which uses the converse idea comparing with the traditional method is presented. The simple analytic solutions of T-H equations are derived, which avoid the secular drift in the traditional solutions and make the formation design in the eccentric reference orbit is as simple as the circular reference orbits. Several formations considering eccentricity are designed and the application fields of formations are easily extended from the traditional circular orbits to the eccentric orbit.Based on the dynamic equations and the orbit constraint, the formation design is systemically investigated that considers the nonlinear relative motion and the eccentric reference orbits. The generalized method is presented and several formations investigated by the linear method are designed again. The secular drifts in previous results are avoided when nonlinearity is considered. Because of the complexity of the formation flying in perturbations, the numeric optimal method is used to design the formation considering perturbations.Using the idea in the classical mechanics, the robust nonlinear control method, named as the constraint force control method, is presented to accurately keep the desired formation arrays. Compare with the other control method, this approach can adequately utilize the characteristic of the dynamic equations, that is, the space natural forces, and accurately keep the arbitrary formation array and satisfy the various formation mission requirements.In this dissertation, the methodology from the system energy view can be applied to the relative motion study of the celestial bodies, the tethered satellites systems, et al. Presented the constraint force control method can be used to the dynamical systems control with the equality constraints.