Spacecraft Formation Control Based On Attitude Orbit Integrated Model Using Dual Quaternion

With the increasing complexity and diversification of space missions,in certain application areas,traditional single large satellites can no longer meet the mission requirements.Small satellites flying in formation and cooperating to complete space missions have gradually become the mainstream.The key technology of spacecraft formation flying is torealize the position and attitude control of spacecraft members.Based on the dual quaternion attitude and orbitintegrated model of spacecraft,the distributed observer design,the attitude orbit coupling control problem and the related collision avoidance problemare studied in this dissertation when the formation communication topology is undirected graph.Based on the master-slave control strategy,a distributed observer is designed to obtain the information of the virtual leader of the formation,and the expected position and attitude trajectory of each member spacecraft in the formation is calculated according to the observed information.Combined with the distributed observer,the corresponding generalized PD controller is designed to realize the attitude orbit coupling control of spacecraft formation.The simulation results show that the distributed observer can accurately observe the pilot information,and the corresponding generalized PD controller can effectively track the desired position and attitude.Considering the actual situation that the output of spacecraft actuator is limited and the spacecraft state is limited,the model predictive control algorithm,which is easy to deal with the state constrained problem,is applied to the formation pose control problem in this dissertation.The piece-wise affine linearization method is used to linearize the dual quaternion attitude orbit coupling model,and a model predictive controller is designed based on the linearized model.The simulation results show that the proposed algorithm can effectively track the desired position and attitude of formation under the condition of limited output.In the simulation of the basic model predictive control algorithm,it is found that in the initial stage of the control process,the speed error,angular velocity error,position error and attitude error interact with each other.In other words,the purpose of control is conflict.This conflict results in slow convergence of system error.In order to improve the convergence speed of the basic algorithm,a dynamic weight updating strategy is proposed,which weakens the conflict in the early stage of control process,and greatly improves the convergence speed of model predictive control algorithm.In addition,considering the collision problem that may occur in the formation transformation process,the collision avoidance controller based on artificial potential function is designed to keep the distance between spacecraft members beyond a safe distance.At the same time,aiming at the problem that the instantaneous output of the collision avoidance controller using common potential function is too high and the controller output is not defined when the distance between spacecraft is less than the safe distance,a new derivative function of potential function is proposed,which exchanges the smaller output with long action time,and defines the output value of the controller within the safe distance.Compared with the controller using the common potential function,the improved collision avoidance controller is more in line with the actual application scenario where the actuator output force is limited.