Finite-time Coordination Control For Formation Flying Spacecraft

Spacecraft formation flying(SFF) that has the advantages of the lower cost, higher system reliability, and more flexibility has been widely used in space missions such as deep space exploration and earth monitoring. SFF is an important research direction of the spacecraft technology. Distributed coordinated control algorithm is the core technology and guarantee of SFF. This paper investigates distributed finite-time attitude coordination control laws and distributed finite-time coordination control laws with coupled attitude and translational dynamics for SFF by using the consensus algorithm, control strategy based on behaviors, finite-time control and algebraic graph theory when the attitude dynamic model is established based on rotation matrix. The main contents are as follows.Firstly, distributed finite-time attitude coordination controllers are investigated for formation flying spacecraft without external disturbance. The full state feedback distributed finite-time attitude coordination control law is designed by using the homogeneous theory under undirected graph. Further, the distributed finite-time attitude coordination control law without angular velocity is proposed by using a filter. Theoretical analysis shows that both two coordination controllers can ensure that the system is almost globally finite-time stable. In order to deal with saturation problem, the full state feedback distributed finite-time attitude coordination control law and the output feedback distributed finite-time attitude coordination control law under actuator saturations are given by using the saturation function. All of the finite-time controllers only demand topology structure as an undirected graph, and there is no other additional requirements. In addition, the controllers do not contain the inertia matrix, which has a strong robustness to the inertia matrix.Secondly, distributed finite-time attitude coordination controllers are investigated for formation flying spacecraft with external disturbance under connected undirected graph by using the terminal sliding mode control and adaptive control. The robust distributed finite-time attitude coordination controllers are designed to compensate external disturbances with known and unknown bounds, respectively. The system is almost globally finite-time stable by selecting the appropriate terminal sliding mode surface. In order to deal with saturation problem, the distributed finite-time attitude coordination control law under actuator saturations is given based on the terminal sliding mode, hyperbolic tangent function and auxiliary system. All of the finite-time controllers can solve the algebraic loop problem, and reduce the additional burden of wireless transmission.Thirdly, distributed finite-time attitude coordination controllers are investigated for formation flying spacecraft with external disturbance under directed graph by using the terminal sliding mode control, backstepping and adaptive control. The robust distributed finite-time attitude coordination controllers are designed to compensate external disturbances with known and unknown bounds by using the terminal sliding mode control and adaptive control, respectively. Because of the complexity of the directed graph constraints, both two controllers can not solve the algebraic loop problem. Further, The finite-time coordination controllers are designed to compensate external disturbances with known and unknown bounds by using the terminal sliding mode control backstepping and adaptive control, respectively, which can solve the algebraic loop problem, and reduce the additional burden of wireless transmission.Finally, distributed finite-time coordination controllers with coupled attitude and translational dynamics are investigated for formation flying spacecraft under undirected graph by using the homogeneous theory, filter, terminal sliding mode control, and auxiliary system. The full state feedback distributed finite-time coordination control law is designed by using the homogeneous theory under undirected graph when the dynamic model is without external disturbance. Further, The output feedback distributed finite-time coordination control law is proposed by using a filter. Both two controllers only demand topology structure as an undirected graph, and there is no other additional requirements. Theoretical analysis shows that both two coordination controllers can ensure that the system is almost globally finite-time stable. In addition, the controllers do not contain the inertia matrix, which has a strong robustness to the inertia matrix. The robust distributed finite-time coordination control law and the distributed finite-time coordination control law under actuator saturations are given based on the terminal sliding mode and auxiliary system, respectively, when the dynamic model is with external disturbance. All of the finite-time controllers can solve the algebraic loop problem, and reduce the additional burden of wireless transmission.