Optimal Control For Satellite Formation Establishment Of Flying-around In Elliptic Orbit

The two-body spacecraft formation in elliptical orbit is studied in this work.With a purpose of establishing the flying-around formation configuration,the conditions of initializing the periodic relative trajectories in elliptical orbit are analyzed.After that,the three dimensional geometric characteristics of the periodic relative trajectory,as well as the trajectory projections in the coordinate planes,are discussed in details.By involving the multiple deployment constraints,the optimal deployment problem for establishing the flying-around configuration is formulated and solved via Gaussian Pseudospectral method.The work is organized as follows:Firstly,the nonlinear high-precision relative orbital dynamics that describing the relative motions in elliptical orbit are developed with respect to the inertial frame,then by using the variable transformation,the dynamics are linearized and the analytical solutions is obtained.Based on the analytical solutions,different types of relative trajectory are discussed and the periodical conditions for relative motion are derived.The results indicate that the periodic relative trajectories commonly occur as three-dimensional curves.With a further variable transformation,the complicated periodic solutions are algebraically solved,and four types of stable formation configurations are proposed based on geometrical regularity identifications.Furthermore,in order to enable the three-dimensional inspection on the chief spacecraft,the flying-around formation configuration is proposed by defining the initial conditions of the relative dynamics.Secondly,we attempt to deploy the deputy spacecraft into the flying-around trajectory,within which the three dimensional inspection on the main spacecraft can be performed.Based on the relative dynamics and the periodical conditions,the optimal deployment problem for the deputy spacecraft is formulated.To make the deployment more realistic,the constraints on the propulsion amplitude and the camera surveillance are also considered.In order to find the numerical solutions,the optimal deployment problem with multiple constraints is discretized by using straightforward domain-transformation technique.Finally,a series of simulations are carried out to demonstrate the effectiveness of the proposed method.The optimal deployment of the deputy spacecraft is numerically solved by minimizing the control effort.The deployment trajectories,as well as the control profiles,are analyzed under different constraints.After that,the sensitivities of some important parameters on the deployment are also discussed based on numerical results.