Relative Trajectory Optimization And Control For Satellite Formation Flying

Formation flying satellites can achieve the acquisition,processing and analysis of space data by the coordination between satellites,thus accomplishing a number of complex space mission and have a broad prospect in space science,application and security.At present,the large scale formation flying for low-cost micro-nano satellites and the high stability formation flying for spacecraft in the deep space orbit are the promising and emerging topic among formation flying.The foundation of satellites formation flying dynamics and control is a well-designed geometric configuration,but the key and challenge is the autonomou and coordinated control of formation flying satellites.Formation configuration design,the analytical control method of formation flying satellites,the trajectory optimization for formation reconfiguration and the coordinated control of formation flying satellites are studied in the dissertation.Firstly,the analytical expressions of the configuration parameters under the J2 perturbation are deduced using the non-singular orbital element,and the stable condition and formation design method under J2 perturbation are introduced,which have laid a theoretical foundation for formation keeping control.Moreover,the deep space formation configuration optimization model considering the third-body perturabtion and mission constraints is established based on the relative equation with the orbit element difference,and the satisfied equilateral triangle configuration for space gravitational observation is obtained by combing the differential evolution algorithm and the sequential quadratic programming algorithm.Secondly,the non-singular orbital element differences dynamics equation considering the J2 perturbation and the coupling effect between in-plane and out-of-plane relative motion is derived,and the mixed integer optimization problem is solved with the genetic algorithm and the sequential quadratic programming algorithm.Afterwards,the feasibility of the method is verified,compared with the nonlinear impulsive trajectory optimization method and primary vector theory under J2 perturbation.Additionally,the necessary condition and analytical gradient matrix considering third-body perturabation for the low-thrust tranfer orbit optimization is derived based on the Pontryagin Maximum Principle,and the problem is solved with the homotopy method.At the same time,with the priciple of energy-optimal,the transfer trajectories optimization model considering the fuel balance and the escape orbital parameters are obtained for the space gravitional wave detection.Then,in terms of the analytical and loose formation keeping control of the near Earth orbital satellites,the mean relative velocity is used to denote the drift rate of satellite formation,and the analytical expression between the average relative velocity and the incremental velocity is derived.Based on it,an analytical control strategy that only requires inter-satellite ranging information is proposed under J2 and atmospheric drag perturabation,which is suitable for realization in engineering and on-board calculation.Besides,a collision warning algorithm and collision avoidance algorithm based on Newton iteration are proposed and the simulation results show the effectiveness of the algorithm.In addition,the mechanism of the in-track drift caused by the normal maneuver of formation satellites is clarified,an analytical in-track compensation method is proposed,and the effiectiveness is verified by the application example in a geomagnetic field detection project.Finally,a distributed and coordinated architecture for the multiple near-Earth formation flying satellites is designed based on the virtual structure and consensus theory,in which the coordination variables are instantiated based on the formation configuration design method.Furthermore,the "switching" control of the control sequence is realized by combining with linear quadratic control and pseudo-rate control.The simulation shows that for the bidirectional ring network communication topology,it can be guaranteed by the consensus algorithm that the formation team obtain continuous cooperation information,thus achieving consensus symptotically.