Energy-optimal low-thrust satellite formation manoeuvre in presence of J₂ perturbation

This article proposes a method to determine energy-optimal low-thrust trajectories for satellite formation manoeuvre in the presence of the J ₂ effect. This manoeuvre is cast as a nonlinear optimization problem with a desired final satellite formation configuration subjecting to collision avoidance constraint. With this proposed approach, the deputy satellite is manoeuvred into a quasi-periodic desired final formation with respect to the chief satellite in the presence of the J₂ effect. Resulting non-linear optimal control problem is converted into non-linear programming (NLP) problem by a direct transcription method called Legendre pseudospectral method. The NLP problem is then solved using a sparse non-linear optimization algorithm. Simulation results validate the proposed optimal trajectory design for formation manoeuvres in the presence of the J₂ effect.