Distributed Fixed-time Coordinated Control For Spacecraft Formation Flying

A spacecraft formation flying(SFF)system consists of multiple simple and small spacecraft and accomplishes complex space missions by the information interaction and cooperative coordination among spacecraft.Spacecraft formation flying has the advantages of easy manufacture,low maintenance cost and high reliability,which is widely used in the fields of earth survey and deep space exploration.Finite-time control techniques can provide fast convergence rate,strong robustness and strong disturbance rejection properties,but the upper bound of convergence time is dependent on the initial condition,which implies that the convergence time grows unboundedly when the initial state tends to infinity from the equilibrium and the convergence time could not be predicted when the initial state could not be obtained.As a special finite-time control,fixed time control not only has the advantages of the former,also confines the convergence time independent of initial states but only related to design parameters,which is significant in the engineering application.Some spacecraft formation missions,such as Techsat-21 Mission,are required to achieve attitude synchronization and formation configuration in the specified time,thus research on fixed-time coordination control for spacecraft formation flying is significant.This paper investigates fixed-time attitude coordination control and fixed-time coordination control with coupled translational and rotation dynamics.Based on the distributed structure and algebraic graph theory,fixed-time coordinated control algorithms are designed by utilizing the terminal sliding mode control,homogeneous theory,the integral sliding mode control and adaptive control.Given the analysis and discussion above,the main contents are presented as follows.Firstly,based on the fast terminal sliding mode(FTSM)and nonsingular fast terminal sliding mode(NFTSM),a novel terminal sliding manifold is proposed which achieves fixed-time convergence,and could be applied in distributed coordination controller design for spacecraft formation flying.Distributed fixed-time attitude coordination problems are investigated for formation group members without external disturbance and with unknown bounds’ disturbance respectively.Under the undirected graph,distributed fixedtime attitude coordination controllers are designed for group members without external disturbance by using the fixed-time terminal sliding manifold.The fixed-time stability of the closed-loop system is ensured by employing the Lyapunov method.When group members require the neighbours’ control input information,an algebraic loop yields.Inorder to solve the problem,a fixed-time sliding mode estimator is constructed to estimate leader’s attitude.Based on the proposed sliding mode estimator and adaptive control technique,distributed fixed-time attitude coordination controllers are given for group members with unknown bounds’ disturbance,which achieve fixed-time convergence of the system and avoid the algebraic loop problem.Secondly,a novel integral sliding mode is proposed based on homogeneous theory,which provides bounded convergence time independent of initial conditions and ensures total robust of the system by eliminating the reaching phase.By using the integral sliding mode and the disturbance observer,distributed fixed-time attitude coordination control is investigated for group members with known bounds’ disturbance.In order to avoid the algebraic loop problem and reduce the communication burden among members,a fixedtime sliding mode estimator is constructed to estimate the leader’s attitude state.Under undirected connected graph,distributed fixed-time robust attitude coordination controllers are designed by utilizing the sliding mode estimator,integral sliding mode and the disturbance observer,and global fixed-time stability of the closed-loop system is guaranteed by Lyapunov technique.Thirdly,distributed fixed-time output feedback attitude coordination problem is investigated for group members without angular velocity measurement by using the homogeneous theory and integral sliding mode control.The fixed-time state observers are designed to estimate unmeasured angular velocity information of members,and the fixedtime stability of observation error systems are ensured based on homogeneous theory and Lyapunov method.Under undirected graph,distributed fixed-time output feedback attitude coordination controllers are proposed by using sliding mode estimator,fixed-time observer and the integral sliding mode,and ensure that the system is semi-global fixedtime stable.Finally,fixed-time coordination control for group members with coupled translational and rotation dynamics are investigated,and distributed fixed-time coordination controllers are designed for members without external disturbance and with unknown bounds’ disturbance respectively.Under undirected graph,distributed fixed-time coordination controllers are proposed for members without external disturbance,and the local fixed-time stability of the closed-loop system is ensured by using the homogeneous theory and Lyapunov method.Based on the terminal sliding mode and adaptive control,distributed fixed-time coordination controllers are given when the dynamic models are under unknown bounds’ disturbance,which ensure fixed-time convergence of the sys-tems.Meanwhile,the algebraic loop problem is avoided by appropriate selection of the terminal sliding mode.