Performance Analysis And Information Topology Design For Large Scale Spacecraft Formation Coordinated Control

Coordinated control plays an important role in implementing on-orbit missionsfor spacecraft formation while the basic premise is the inter-satellite informationexchange. For large-scale formations composed of a dozen or dozens of memberspacecraft, distributed coordinated control strategy via local information exchange isalways considered in order to reduce the amount of inter-satellite informationexchange. Since inter-satellite information exchange has great effect on formationcontrol system performance, it’s an urge to analyze the system performance from theperspective of information topology and to provide with valid topology designmethods for the system design of large-scale spacecraft formation. In thebackground of large-scale formation flying with leader-follower structure，toolsfrom graph theory are employed to investigate system performance of formation thatused the consensus-based protocol. Methods on information topology design areinvestigated with the aim of performance improving. The major contents of thedissertation are as follows:For formations with leader-follower structure, controllability of each followerunder the leaders’ actions is a key influencing factor of formation missionimplementation. For large-scale formations with multiple leaders and directedinformation topology, tools including weakly connected components are used todecompose the controllability problem of the whole system to that of severalsubsystems and hence greatly simplify controllability analysis. Sufficient ornecessary conditions on formation controllability are also studied based on theeigenvalues of the Laplacian matrix. In addition, the interactions between memberspacecraft are characterized with the aid of relaxed equivalent cell partition. Weprove that it’s a necessity for controllable formation that each cell of the relaxedequivalent partition of the information topology can only contain one followerspacecraft. Based on the analysis, common approaches are presented to attaincontrollable formation. Information topologies are also designed to meet thedemands of controllability.Formation missions such as fractionated formation have no strict requirementsof members’ positions and orientations but keeping them in a certain target area. Forsuch formation missions, containment control is a closely related field and providesfeasible solutions. Thus we study formation orbit containment and attitudecontainment problems, and constraint conditions on control gains as well asformation information topology are investigated to provide guidelines for system design. Firstly, an orbit containment control algorithm is proposed and necessaryand sufficient conditions on convergence are presented based on the systemLaplacian eigenvalues. It is revealed that each follower must be reachable from atleast one leader to ensure containment objective. Secondly, attitude containmentcontrol problem is investigated in the case where attitude orientation topology andangular velocity topology are distinct. Constrained conditions on the attitudeorientation information topology and angular velocity information topology arederived to ensure containment by using Lyapunov method.Convergence rate is an important index of system performance. For theproposed orbit containment control algorithm, influences of the control gain and theformation information topology on system convergence rate are investigated. Inaddition, design methods of the control gains and the system information topologyare presented to improve system convergence rate. Specifically, for bidirectionalinformation topology, control gains which achieves maximal convergence rate aregiven, and it is proved by using Weyl lemma that system convergence rate can beimproved by either adding bidirectional edge between followers or directional edgefrom leader to follower. For unidirectional information topology, convergence rateis specified and it is proved that the convergence rate can be characterized by thesmallest nonzero eigenvalue of a new topology constructed from the originalformation information topology.In formation containment problem, the followers’ distributions in the targetarea should satisfy some requirements for collision avoidance or communicationlink establishment. Since the followers’ steady states are determined by theformation information topology, formation information topology design problemson followers’ steady states are studied. The reachable set of the leaders areemployed to analyze the followers’ steady states, and it is proved that eachfollower’s steady state is a convex combination of the states of the leaders whichcan reach the follower. Moreover, two kinds of cell partitions of the formationinformation topology are defined to investigate the followers’ steady states. It isproved that followers that belong to the same cell will have the same steady states.Besides, it is revealed that information exchange within the cell has no effects on thefollowers’ steady states, which means formation performance can be improved bydesigning information exchanges within each cell. Finally, information topologiesthat meet different mission requirements are designed.