Coordinated Control Methods For Spacecraft Formation Flying Under Time Constraints

With the development of large-scale space missions,using multiple spacecraft to complete complex space missions instead of a single large spacecraft is a research hotspot in the current space field,which also puts forward higher requirements for spacecraft attitude and orbit control.In the process of spacecraft formation flying,it is not only necessary to achieve high-precision attitude coordination and space configuration maintenance,and it is also hoped that the coordinated control of spacecraft can be completed within a limited time or even a prescribed time.Based on the formation missions,such as distributed SAR system and deep space interferometer,this paper explores the coordinated control method of spacecraft formation under time constraints,and focuses on the problems of actuator failure,unkonw leader information,without anguar velocities measurement,image-based attitude-orbit integrated control and so on.The main research contents are as follows.Aiming at the possible actuator failure of spacecraft formation flying,a finite time fault-tolerant attitude coordinated control scheme based on directed graph is proposed.Assuming that only some spacecrafts can receive the attitude information of the leader,a finite time state observer is designed for each following spacecraft to estimate the attitude information of the leader.Using the homogeneous property and Lyapunov method,it is proved that the observation error can converge to a small field in a finite time.Considering the actuator failure and bounded uncertainty of inertia moment and external disturbance,a adaptive law and distributed finite time fault-tolerant attitude cooperation controller are designed.The finite time stability of the closed-loop system and its robustness to actuator faults and external disturbances are analyzed by combining sliding mode control and Lyapunov method.Finally,the proposed attitude fault-tolerant finite-time control scheme is verified by numerical simulations,and compared with asymptotic controller and non-fault-tolerant finite-time controller,the superiority is illustrated.Since the convergence time of the finite time control scheme depends on the initial state of the system,the fixed-time attitude coordinated control strategy is studied for the problem that only part of the followers can receive the attitude information of the leader and unkonw the angular velocity measurement.Because only some followers can directly receive the leader’s attitude information,a distributed fixed time observer is designed to estimate the leader’s attitude information,so that each following spacecraft can obtain leader’s attitude information in a fixed time.Considering that the angular velocity information of follower spacecraft is difficult to measure and there are unknown external disturbances,a fixed time extended state observer is proposed to estimate the above information online.A distributed fixed time attitude coordinated controller is further designed.Using homogeneity and Lyapunov method,it is proved that the spacecraft flying in formation can achieve attitude consensus in fixed time under the action of the proposed controller.Finally,the effectiveness of the proposed fixed time control scheme is verified by numerical simulations,and the performance is compared with the finite time controller to prove the advantages of the fixed time control scheme in convergence speed of convergence accuracy and coordination.Because the convergence time of both finite time and fixed time control depends on the designed parameters,the convergence time of spacecraft formation system cannot be set arbitrarily,so the prescribed time attitude coordinated control strategy of spacecraft formation is further studied.Considering that only a set of follower can directly obtain the attitude information of the leader,a distributed prescribed time observer is designed for each follower to estimate the attitude information of the leader.Based on time-varying scaling function,sliding mode control theory and prescribed time observer,a distributed prescribed time attitude coordinated control algorithm is designed under undirected communication topology.The stability of the closed-loop system is proved by Lyapunov method,the effectiveness of the proposed prescribed time attitude coordinated control scheme is verified by several numerical simulations,and compared with the fixed time controller,which shows that the actual prescribed time control scheme has obvious advantages in reducing control torque and energy consumption.Aiming at the problem of integrated attitude-orbit coordinated control of spacecraft formation,an image-based finite time control strategy is proposed.Based on the two-dimensional image information,a 6-DOF relative motion dynamics model of spacecraft is established.The model avoids the process of relative pose estimation,and the image features are directly used in the controller design.When the real-time target image matches its corresponding reference image perfectly,it can be considered that the following spacecraft has realized the position tracking and attitude synchronization of the leader.A fast terminal sliding mode variable is defined by using image features and its rate,and a finite time coordinated controller is designed according to the sliding mode variable.In order to improve the accuracy of formation configuration,a coordinated term is introduced into the controller to reduce the relative pose error between followers.Considering the system uncertainty caused by leader maneuver and external disturbance,the robust term is further introduced into the controller to suppress the uncertain factors in the dynamic model.The stability of the closed-loop system is analyzed by Lyapunov method and algebraic graph theory,and the performance of the controller is evaluated by mathematical simulation for a typical formation flying scene.