Collision Prediction And Avoidance Control For Satellites In Formation Flying

Formation flying defined by the distributed satellites consisted of many small satellites flying in formation to perform space mission together is equivalent to the capability of a large virtual satellite. Comparing with the traditional satellites, satellites in formation flying show vast application vista due to the dominate advantages in many aspects. The orbits configuration of satellites in formation flying need to design to avoid potential collisions that may occur when a satellite within the formation drifts into the path of another, or when foreign objects enter the formation.Being differ from the relevant study based on circle reference orbits at present, the prediction of the collision probability and a control strategy to avoid collision for formation flying in eccentric reference orbits are presented in this paper. The derivation of Lawden equation describing the relative motion for formation flying in eccentric orbits is introduced to obtain the periodicity conditions. The Symplectic perturbation method based on precise integration of the fundamental interval is developed. In this frame the prediction of linear time-varying system, namely the Lyapunov differential equation with variable coefficients, is able to be solved. Numerical examples show that Symplectic perturbation method is provided whit high precision and excellent numeric stability due to the symplectic conservation. This paper creates the collision model based on Lawden equation. A general prediction method for calculating the collision probability for formation flying in eccentric orbits is given and the influences by uncertain initial conditions, uncertain environment disturbance, orbital eccentricity ratio etc. are observed. A control strategy to avoid collision while minimizing the energy required for the maneuver, namely the instantaneous correction velocity method, is discussed then applied in avoidance control for satellites in formation flying in eccentric orbits. Numerical examples prove its validity.The major work of this paper: The collision prediction based on the symplectic conservation method for satellites in formation flying in eccentric orbits and the relevant avoidance control strategy. Some suggestions for the next study are presented in the last section.