Research On Coordinated Control Of Multi-Spacecraft Formation Flying Based On Algebraic Graph Theory

Formation flying missions such as deep-space optical interferometer demand coordination of up to tens or hundreds of spacecraft in order to fulfil the requirements of black hole event horizon and terrestrial planet observation and so on. While coordinated control is the basic guarantee of accomplishing in-orbit mission of multi-spacecraft formation, the realization of coordination is on the basis of inter-spacecraft coordination information sharing. Due to the restriction of limited field of view, communication bandwidth and range, as well as the influence of mutual occlusion together with spatial electromagnetic and mechanical environment, the information-sharing links resulting from optical measurements or communication may be unidirectional, sparse and unreliable. Conditions with such limited information sharing not only restrict the coordination approach, but also affect the coordination capability or even de-stabilize the formation, which make it a pressing issue for future multi-spacecraft formation flying missions. In the context of multiple formation flying spacecraft with limited information sharing, algebraic graph theory along with consensus theory of multi-agent systems arisen in recent years are taken in this dissertation for in-depth study on its orbital coordination and attitude coordination. The study is focused on the analysis of system stability and coordination capacity under the limited information sharing in order to provide a reference for further information topology design and coordinated control in the future. Research details are as follows:For multi-spacecraft formation flying in deep space, it’s a prerequisite for successful mission performance to exert control over relative orbit to maintain a stable geometric pattern under the limited information sharing condition. In the context of a multi-spacecraft formation in the L2 libration point of the Sun-Earth/Moon system, and in view of the unidirectional sensing of relative states together with the sparseness and time-variability of the formation information topology, a two-hop neighbor information sharing approach is first proposed and an orbit coordination algorithm using only relative measurements is designed afterwards. Algebraic graph theory and matrix eigenvalue theory are taken to analyze the stability of the system with fixed directed topology, time-varying topology and input delay respectively. It is found that, if there exists no time delay or the delay is limited, coordination can be attained if the formation information topology contains a directed spanning tree. To strengthen the robustness to time-varying topology as well as to overcome the two-hop neighbor information requirement of the foregoing controller, an orbit coordination controller using nearest neighbor information is further designed. By introducing an equivalent coordinate transformation, the closed-loop system is converted to an exponential stable system cascaded by a first-order consensus algorithm, and then theory on first-order consensus is used to analyze the stability and robustness to time-varying topology. It is shown theoretically that coordination can be achieved if the formation information topology is uniformly quasi-strongly connected, and the constraint on the controller parameter imposed by system stability is independent of the information topology, which hence strengthens the robustness to the switching of the topology. Furthermore, upper bound of the controller is also given so that a reference is provided for the controller parameter design under control input saturation.In order to accomplish missions like beam synchronization or distributed interferometric imaging, coordination of relative attitude between member spacecraft is a problem that must be addressed. For multi-spacecraft formation with attitude information sharing by inter-spacecraft communication, the unidirectivity and the sparseness together with time-variability of the communication topology should be taken into account. On the basis of the model of networked Euler-Lagrange system, adaptive attitude coordination controllers are designed using a first-order consensus algorithm and a second-order consensus algorithm respectively. The ability of coordination under directed communication topology especially time-varying topology that is uniformly quasi-strong connected is demonstrated strictly, and the stability of system with parametric uncertainties is also given. On these bases, a general framework for attitude coordination controller design is further proposed using Euler-Lagrange equation and its properties. Integral input-to-state stability and set stability are taken to prove that attitude coordination controller design in this case is equivalent to the design of a consensus algorithm under the framework, which means the attitude coordination problem of spacecraft is converted to a consensus seeking problem that is independent of its nonlinear dynamics. Separation of limited information sharing constraint from the nonlinear dynamics constraint in the design process of attitude coordination controller is achieved, and hence, with the framework, research emphasis can be put on the influence of the information-sharing topology and its constraints using model of linear dynamics. By substituting first-order consensus algorithm with/without leaders to the framework respectively, two attitude coordination controllers that are coincident with the results designed using traditional approaches are obtained, which hence validates the proposed general design framework.For multi-spacecraft formation system, fault probability of gyros increases. And in view of cost restriction, it is hard and unnecessary to equip each member spacecraft with a set of precision gyros. With this knowledge, several attitude coordination algorithms for multi-spacecraft formation with limited information sharing and without angular velocity feedback are proposed. By combining with feedforward and feedbackward control, a quaternion-based output feedback attitude coordination controller is first designed using lead filters. The global asymptotical stability is analyzed either when the reference attitude is known globally or when the formation information topology is an undirected tree. Reduction property is also demonstrated with La Salle invariance principle. Then, using non-redundant MRPs(modified Rodrigues parameters), a model-independent dynamic output feedback regulator is designed based on Euler-Lagrange equations. Homogeneous theory together with algebraic theory is used to prove its finite-time convergence. To solve the actuator saturation problem, hyperbolic tangent function is used to give a modified bounded attitude coordination controller. Finally, mathematical simulations are conducted to validate the effectiveness of the proposed controller.