Variable state size optimization problems in astrodynamics: N-impulse orbital maneuvers

Abstract

This paper details recent results in variable state size optimization problems in astrodynamics. The application presented in this paper is fueloptimal N-impulse orbital maneuvers. Previous work required the user to choose the number of impulses, N, while the current work considers N as a variable to be optimized, making the state size a variable throughout the optimization process. It is well known that for N > 2, a numerical optimization method is required for a general solution to the orbit transfer problem. Two algorithmic approaches are presented such that they may be used with a variety of numerical optimization techniques. The first structure runs an outer problem which optimizes the number of impulses, thus determining the length of the state vector, while an inner problem optimizes the orbital maneuver for the given number of impulses. The second structure incorporates the variable N into the state vector to be optimized, leading to a dynamic state vector length. This structure causes some properties of any given numerical optimization method to necessarily be modified. For example, the evolutionary operators must be able to deal with states of different lengths. Examples are provided that show new scenarios under each structure and show agreement with examples from the literature.