A new approach for low-thrust trajectory design for GEO to Halo transfer in three-body problem

In this study, a new approach is proposed to design low-thrust trajectory in the preliminary design phase for GEO to Halo transfer in the three-body problem. In this method, the approximate and near optimal trajectory is conducted through guessing thrust angles. In this approach, the in-plane and out of plane thrust angles are considered as finite Fourier series with unknown coefficients. The coefficients are calculated by an optimization algorithm with the aim of minimizing mission duration. Since the number of the trajectory revolutions is unknown, this parameter is also considered as a discrete decision variable of optimization algorithm. Due to the existence of continues and discrete decision variables, discrete particle swarm optimization algorithm is employed to solve the problem. The advantages of this method include: simplicity of execution and low volume of mathematical computation, considering satellite mass, do not assume special restriction for thrust angle such as tangential thrust and determination the near optimal mission duration. . In order to evaluate the proposed method, Trajectory design of GEO to Halo is performed for several level of thrust. Results indicate that this approach determines the number of trajectory revolutions, fuel consumed, near optimal duration and trajectory of the mission with high accuracy.