Distributed Coordinated Control For Multiple Spacecraft Formation Flying

Formation flying for multiple spacecraft refers to a system of several spacecraft flying in orbit within a particular formation shape, which could realize cooperative work among the spacecraft by inter-satellite communication. Compared with traditional monolithic spacecraft, spacecraft formation flying has the advantages of strong flexibility, high reliability and low cost, and it is capable to accomplish more complex space missions. Therefore, spacecraft formation flying has a wide application prospects in both military and civil fields. To guarantee completing the formation flying missions, effective coordinated control approaches are the key technologies. This dissertation surveys the existing research achievements, and gives a deep study on the problem of coordinated control for multiple spacecraft formation flying by using algebra graph theory, consensus algorithm and nonlinear system theory. The main contents are summarized as the following several parts:The attitude tracking coordinated control problem for multiple spacecraft formation flying under an undirected communication topology is investigated based on the rotation matrix model. Firstly, a "proportion plus derivation plus feedforward compensation" attitude coordinated controller is proposed when external disturbances are zeros. Under the controller, the spacecraft can track the desired attitude and angular velocity, while keeping the relative attitude of other spacecraft to some extent. Further, using the error analysis of attitude vector measurements, an attitude coordinated control strategy with the robustness of external disturbances is proposed when vector measurement of attitude is adopted. And the robustness of the controller to constant communication delays is studied. The region of attraction, which is satisfied by the system initial values, is presented to realize attitude coordinated tracking with and without communication delays.The attitude coordinated tracking control approaches for multiple spacecraft formation flying under a directed communication topology are investigated based on the rotation matrix model, and the attitude coordinated tracking control problem with model uncertainties, external disturbances, and communication delays is solved. Firstly, the ideal condition without model uncertainties, external disturbances, and communication delays is studied. By introducing an auxiliary intermediate variable including attitude and angular velocity tracking error, an attitude coordinated controller with almost global asymptotical stability is designed. For the condition with model uncertainties and external disturbances, adaptive laws are designed to estimate the unknown inertia matrix of spacecraft and boundedness of disturbances, and adaptive robust coordinated controller is designed. For the condition with model uncertainties, external disturbances, and communication delays, the delayed adaptive robust coordinated controller is designed. By constructing a proper Lyapunov-Krasovskii function, the sufficient condition satisfying stability of the system is provided. The resulting three controllers are all almost globally asymptotically stable and continuous, namely, the system is asymptotically stable under a strongly connected directed graph when the initial value of system lies in the global space except a set of measure zero.When spacecraft can not obtain external reference attitude signals, the autonomous attitude coordinated control methods for multiple spacecraft using only local relative information are proposed under the communication topology of undirected tree. By using the idea of backstepping control design, the coordinated controller is given with the ideal condition, and the control input need only angular velocity and local relative attitude information resolved in the body frame. For the condition with model uncertainties and external disturbances, adaptive laws are designed to estimate the unknown parameters and adaptive robust autonomous coordinated control strategy by using hyperbolic tangent function to attenuate the effects of disturbances. Finally, for the condition with model uncertainties, external disturbances, and communication delays, the adaptive robust autonomous coordinated control algorithm with input constraint is designed by using the idea of command filter. The resulting controllers are all almost globally asymptotically stable and continuous. In other words, the system is asymptotically stable and autonomous attitude coordination is achieved under a strongly connected directed graph when the initial values of system lie in the global space except a set of measure zero.The relative position coordinated control problem for multiple spacecraft system is investigated to achieve multiple control objectives such as formation tracking, formation keeping and collision avoidance. By using local inter-spacecraft information interaction, a relative position coordinated controller for formation spacecraft is designed based on the backtepping control approach. Under the controller, the formation spacecraft can achieve overall maneuvering while keeping the invariance of formation configuration. Further considering control input constraint, model uncertainties, and external disturbances, an adaptive robust controller with control constraint is designed based on command filter and adaptive control theory. For the requirement of collision avoidance for spacecraft formation, two adaptive control strategies are proposed with the unknown mass of spacecraft based on potential function and adaptive control theory, with and without reference trajectory respectively. When no reference trajectory is considered, we prove the spacecraft can achieve consensus of velocity and collision avoidance. When considering the reference trajectory, by choosing a reasonable potential function and designing novel auxiliary variables, we prove that the system can achieve collision avoidance and velocity consensus, and the desired objective lies in the convex closure of formation spacecraft eventually.