Research On Relative Position And Attitude Measurement And Control For Formation Micro-satellite Based On Dual-Quaternion

Multi-micro satellites formation flying has the advantage of high reliability, strong flexibility and high performance price ratio and is regarded as trend about spacecraft technology. In satellites formation flying, the traditional method is to measure and control the orbit and attitude respectively, which increases the complexity of measurement and control systems.Dual quaternion describes space position information and rigid body attitude information uniformly,then it simplifies the operation.This dissertation established relative kinematic equations for formation satellites based on dual quaternion, and based on that established relative position and attitude update algorithm and machine vision-based relative position and attitude measurement algorithm. Besides, this dissertation established relative dynamics equation based on dual quaternion. On this basis it proposed relative position and attitude control algorithm for leader-follower formation satellites and cooperative control algorithm for multi-satellites formation. The main contents and innovations are as following:(1) This dissertation analyzes the relative motion theory of the formation flying satellites, establishes relative kinematics and dynamics models, and the relative attitude kinematics and dynamics model based on quaternion.(2) Relative position and attitude representation for formation satellites based on dual quaternion has been proposed. As the satellite motion is non-exchangeable, the screw compensation algorithm based on screw theory is designed, which can update relative position and attitude of formation satellites. According to the "analogy" laws, on the basis of "rotation vector", it mainly makes researches and analysis on the "screw vector" of screw algorithm,which can update the dual quaternion, then the screw compensation algorithm can be deduced to complete satellite’s relative position and attitude representation.The screw compensation algorithm doesn’t have to design two sets of coefficients respectively for updating satellite’s relative position and attitude,thus it proves its consistency with traditional algorithm.The optimization algorithm of two-subsample, three-subsample and four-subsample is deduced and using the subsample screw algorithm in simulation.(3) Machine vision-based relative position and attitude measurement algorithm for formation flying micro-satellites has been proposed. For the monocular vision algorithm requires iterative solution, and the convergence of iterative solution affects real time and veracity of measurement, this dissertation uses binocular stereo measurement and dual quaternion to build relative position and attitude error model. Also, it uses Lagrangian method to build auxiliary function to calculate the solution of relative position and attitude information of satellites. Instead of the traditional feature point, we use two non-coplanar feature lines to do measurement, and use Plücker lines to represent the two characteristic lines. Singular value decomposition method is applied to get the dual quaternion value, then the relative position and attitude information can be obtained.The simulation results show that the algorithm unified describes the rotation and translation matrix, which is a real-time and accurate position and attitude measurement algorithm.(4) Coupled control algorithm for satellites formation flying based on slide-mode theory and graph theory has been proposed. According to the uniform attitude and orbit mathematical model, this paper established relative kinematic and dynamics models for formation satellites based on dual quaternion to make researches on the problems in attitude and orbit coupled control law, then a unified formation satellite’s position and attitude determination and coupled control system has been established. The paper proposed a cooperative control algorithm for leader-follower formation satellites used slide-mode theory and for multi-satellites formation used graph theory. The coupled control algorithm doesn’t have to control relative position and attitude information of formation satellites respectively, thus it reduces the complexity of the algorithm. Simulation results show that the position and attitude coupled algorithm is simple and has better tracking control performance.(5) Based on the theoretical research we established a semi-physical simulation platform to verify the correctness of rationality of the theory. PC104 platform micro-satellites systems simulation system is used to build this simulation platform, Vxworks operating system is used to manage this platform. The biggest feature is that we can use one computer to do satellite management as well as satellite attitude and orbit measurement and control. This integrated software design improves the system integration and is more suitable for formation flying micro-satellites.In conclusion, by analying and simulating, it mainly makes researches on the problems in kinematics and dynamics, relative position and attitude measurement, control of micro-satellites formation flying based on dual quaternion, which provide ideas for the research and be of some help to the distributed satellites technique.