Study On Spacecraft Relative Motion Around Non-Keplerian Orbits

Over the last decades,the space technologies have been developing at an unprece-dented rate.As the human activities steps into deep space,the propellant becomes the most critical factor concerning whether the mission could be successfully accomplished or not.In recent years,some novel propulsion systems have been proposed,with the representative ones being solar sails and electric sails which utilize the solar radiation pressure and solar wind reaction respectively.Such sail-based spacecraft are considered well-suited for interstellar explorations because the spacecraft exploits the solar power to generate propulsive thrust without any fuel consumption.Due to these unique merits,the sail-based spacecraft has drawn much attention of many scientific research institu-tions and senior experts.In particular,the solar sails and electric sails enable a class of non-Keplerian orbits which the traditional spacecraft are incapable of,providing an ideal platform for space missions like communications relay,astronomical observation and space physics research.To this end,the current dissertation focuses on the dynamics and con-trol of relative motion around two classes of typical non-Keplerian orbits(i.e.heliocentric displaced orbits and halo orbits),aimed at providing an essential reference for potential space mission applications in the future.The main achievements and contributions are summarized as follows:1)Coordinated solar sail formation flying around heliocentric displaced orbits.To begin with,each class of the solar sail circular heliocentric displaced orbit is reviewed,and their stability conditions are analyzed accordingly.For solar sails equipped with a reflectivity control device,the conditions for creating a planet following displaced orbit are derived,and the feasible regions with the maximum reflectivity rate constraint are numerically found in terms of displaced orbital parameters.The concept of deploying multiple solar sails in formation around elliptic displaced orbits is proposed,and the communication topology of the formation system is characterized by an algebraic graph.Coordinated control strategies are presented for both the full state feedback case and the relative velocity unavailability case,respectively.The developed consensus-based algorithms rely on the protocols formulated on an undirected communication topology with information link couplings,utilizing every available neighbor-to-neighbor information data such that the overall reliability of the formation system can be enhanced.Illustrative results indicate that the designed cooperative control laws ensure an ultimate formation tracking as well as synchronization during transition.2)Coordinated electric sail formation flying around heliocentric displaced orbits.The existing thrust vector models of an electric sail,i.e.the inversely proportional model,the 6-th order poly-fit model and the geometrical analytical model,are revised.The necessary conditions for generating an electric sail-based planet following displaced orbit are derived,and the feasible regions as a function of the orbital parameters are numerically plotted.The mutual information exchange among the electric sail formation system,characterized by the communication topology,is represented by a weighted graph.Two typical cases,according to whether the communication graph is directed or undirected,are discussed.For each case,a distributed coordinated control law is designed in such a way that each deputy not only tracks the chief state,but also makes full use of information from its neighbors,thus increasing the redundancy and robustness of the formation system in case of failure among the communication networks.3)Geometric topology of relative motion between heliocentric displaced orbits.A new set of displaced orbital elements are proposed to characterize the spacecraft along the displaced orbit.Analogous to Keplerian orbital elements,the newly defined set of displaced orbital elements has a clear physical meaning and provides an alternative ap-proach to obtain a closed-form solution to the relative motion between displaced orbits,without the need of linearizing or solving the corresponding nonlinear equations.The invariant manifold of relative motion between two arbitrary displaced orbits is deter-mined by coordinate transformations,thus obtaining a straightforward interpretation of the bounds,namely,maximum and minimum distances of relative position vectors.The extreme values of these bounds are then calculated from an analytical viewpoint,both for quasi-periodic orbits in the incommensurable case and periodic orbits in the 1:1 com-mensurable case.In particular,when the relative orbital elements are 1-st order small,the approximate geometry of the relative motion is also analyzed.4)Distributed adaptive synchronization for multiple low-thrust spacecraft formation flying around libration point orbits.A halo orbit around the libration point is selected as the nominal trajectory of the spacecraft formation system.The nominal halo orbit is first identified by the differential correction method,and then parameterized by truncated Fourier series expansions.Such an explicit,albeit approximate,description of the nominal trajectory facilitates each spacecraft in formation to include the relative state informa-tion into a cooperative feedback control system design,so that the relative motion can be driven towards a desired trajectory while maintaining a group synchronization during maneuvering phase.Distributed adaptive coordinated control strategies are proposed to account for unmeasurable relative velocities and spacecraft mass uncertainties respective-ly.In particular,both time-balanced and propellant-balanced formation maneuver can be achieved with the consensus-based control laws,which is of great importance for mission lifetime extension.