Distributed Coordinated Control For Multiple Spacecraft Systems Under Directed Communication Topology

As the increasing complexity of the space missions, the spacecraft need to becomemore and more powerful. It brings certain risks inevitably to the completion of the spacemission if all features are all integrated into one single spacecraft. Recently, distributedcoordinated control has gained much attention for multiple spacecraft formation flying.Using graph theory, the node represents the spacecraft, and the directed path betweentwo nodes represents the information transmission relationships among the spacecraft,which brings greater convenience to study the distributed coordinated control for multiplespacecraft system. The dissertation surveys the recent results on multi-agent systemsand spacecraft formation flying, and give a deep study on the distributed coordinatedcontrol for multiple spacecraft systems under a directed communication topology. Themain contents and contributions of this dissertation can be summarized as follows:The coordinated tracking problem for spacecraft formation flying under a generaldirected graph is investigated. Two cases have been studied, namely, all the followerspacecraft can obtain the information of the leader spacecraft and only a subset of thefollower spacecraft has access to the leader spacecraft. In the first case, for the errordynamic equations of spacecraft described by the Modified Rodriguez Parameters (M-RP), a nonregressor-based adaptive cooperative tracking control algorithm is proposedfor multiple spacecraft formation flying dealing with modeling uncertainties and externaldisturbances. As a result, all follower spacecraft in the formation converge to the desiredattitude cooperatively and track the time-varying leader spacecraft. In the second case,under the constraint that only a subset of follower spacecraft has access to the leaderspacecraft, a distributed coordinated algorithm is proposed to guarantee that all the fol-lower spacecraft could track the stationary and/or dynamic leader spacecraft. For the casewhere the leader spacecraft has a constant attitude, a distributed controller is developedand it is then extended to achieve relative attitude maintenance. According to Lyapunovstability theory and the input-to-state stability theory, the resulting closed-loop systemsare asymptotically stable as long as the directed communication graph characterizing theinteraction among the followers and the leader contains a directed spanning tree. More-over, for the case where the leader spacecraft has a varying attitude, two sliding-modeestimators are presented for each follower to obtain the estimates of the leader’s attitude and angular velocity using only local information in finite time. Then, an adaptive attitudecoordinated tracking control law is synthesized in the presence of model uncertainties.To improve the robustness of the system and obtain fast convergence performance,we design finite-time attitude coordinated control for multiple spacecraft systems. Forthe leaderless consensus problem, a model-dependent distributed finite-time consensusalgorithm is proposed using feedback linearization theory. On the sliding mode manifold,the finite-time consensus problem for multi-spacecraft systems with second-order non-linear dynamics becomes to the problem for first-order dynamics. For the leader space-craft coordinated tracking problem, a model-independent distributed finite-time attitudecoordination control algorithm for multiple spacecraft formation under a direct commu-nication topology is proposed using fast terminal sliding mode in the case that the leaderspacecraft reference state may only be available to a part of the following spacecraft. Byconstructing Lyapunov function, multiple spacecraft system is proved with global finite-time convergence based on the extended finite time Lyapunov theory and the proposecontrol algorithm can guarantee that the attitudes and angular velocities converge to thedesired values. In order to reduce the chatting of the discontinuous control, the modifiedboundary layer approach was adopted because of the asymptotic stability in the normalboundary layer. The modified control algorithm can guarantee that the attitudes and an-gular velocities converge to a neighborhood of the desired states in finite time. Whenthe leader spacecraft has a constant angular velocity, we propose a distributed continu-ous finite-time estimator and a distributed finite-time adaptive tracking control algorithmto deal with modeling uncertainties and external disturbances. Furthermore, the proposedalgorithm can track the leader spacecraft with a time-varying angular velocity if the leaderspacecraft’s angular acceleration is bounded.Based on the consensus theory, the coupled cooperative control for relative orbitsand attitudes of a multiple spacecraft system is investigated under a directed communi-cation topology. Considering the nonlinear equations for the relative obits of near-earthspacecraft and the attitude motion equations in terms of the MRP, six degrees of free-dom (6DOF) motion equations with coupled control input, unknown nonlinearities, andexternal disturbance are built. In the case where the leader spacecraft state may only beavailable to only a subset of follower spacecraft, we proposes an adaptive L2gain con-trol algorithm based on Chebyshev Neural networks. It is shown that a fleet of followersrendezvous at a fixed point and point toward the same direction. Due to the fact that the relative velocities and relative angular velocities among the follower spacecraft as difcultto be measured, we propose a distributed coupled adaptive control algorithm without us-ing neighbor’s velocities and angular velocities such that all follower spacecraft maintaina desired formation and relative attitudes. In the case that the leader spacecraft are dy-namic, a distributed coupled coordinated tracking control algorithm and an adaptive lawusing only the leader spacecraft state combined with a distributed sliding mode estimatoris proposed subject to input saturation constraints.In this dissertation, the proposed algorithms for each follower spacecraft is onlydependent on its own information and the information of its neighbor spacecraft. Thus,the proposed algorithms are distributed.