Optimization of low-thrust Earth-orbit transfers using the vectorial orbital elements

Abstract As we know, choice of coordinates is of great significance for the performance of analytical and computational approaches in astrodynamics. In this paper, we consider the application of a set of vectorial orbital elements of the Milankovitch type to low-thrust Earth-orbit trajectory optimization and develop a methodology to rapidly work out optimal solutions of low-thrust Earth-orbit transfers. A new vectorial dynamic model of a thrusting spacecraft are presented, and the model is concise and nonsingular for any nondegenerate orbits. A parameter estimation approach is introduced to solve the complex two-point boundary value problem by setting the unknown values of the initial co-states as parameters to be estimated and the boundary values as desired observations. The performance of the proposed dynamic model is demonstrated by optimizing two orbit-raising trajectories and one orbit-lowering trajectory. The simulation results indicate that the proposed dynamic model can give the optimal solutions of low- thrust Earth-orbit transfers with efficiency and robustness.