Adaptive control for spacecraft formation flying with solar radiation pressure and reduction of secular drift

A major problem faced while trajectory planning of spacecraft formation flying is obtaining a “drift-free” case to optimize fuel consumption. The paper considers the effect of non-linearity on relative motion dynamics of spacecraft formation flying with disturbance caused by solar radiation pressure on the formation of spacecraft. The non-linearity is a function of initial conditions, and a perturbation approach is used to correct the initial conditions while maintaining the formation in bounds and also satisfying the zero secular growth requirements. A full state feedback adaptive control law is developed which accounts for the solar radiation pressure, and also estimates and updates the unknown spacecraft mass for formation keeping. The relative dynamics are written as a function of the true anomaly ensuring that the control law works effectively for highly eccentric orbits. Lastly, a Lyapunov stability analysis is shown to ensure the stability of the controller.