Interplanetary transfer optimization using cost function with variable coefficients

In this paper, the optimal interplanetary transfer including planetary escape and capture phases is investigated in the heliocentric frame. Based on primer vector theory, a modified cost function with variable coefficients is developed to reflect the gravitational effect more precisely. The necessary conditions as well as the transversality conditions of the new cost function are derived to search the optimal solution in fixed-time. By introducing the initial and final coasts, the optimal interplanetary transfer is extended to the time-free situation. Finally, the proposed method is applied to the Earth-Mars and Earth-Asteroid transfer. Comparisons with existing methods show that the proposed method can provide better transfer performances with high efficiency. The proposed method extends the application of primer vector theory and provides a fast and accurate reference for preliminary mission design in spacecraft planetary exploration.