Analytic Gradient Computation for Bounded-Impulse Trajectory Models Using Two-Sided Shooting

Ellison, Donald H ; Conway, Bruce A ; Englander, Jacob A ; Ozimek, Martin T

关键词: SPACECRAFT TRAJECTORIES;    TRAJECTORY OPTIMIZATION;    DESIGN OPTIMIZATION;    SWINGBY TECHNIQUE;    FLYBY MISSIONS;    FUNCTIONS (MATHEMATICS);    ANALYSIS (MATHEMATICS);    KEPLER LAWS;    JACOBI MATRIX METHOD;    FLIGHT TIME;   

RP-ID  :  GSFC-E-DAA-TN42078-1

学科分类：天文学(综合)

美国|英语

来源: NASA Technical Reports Server

【 摘 要 】

Many optimization methods require accurate partial derivative information in order to ensure efficient, robust, and accurate convergence. This work outlines analytic methods for computing the problem Jacobian for two different bounded-impulse spacecraft trajectory models solved using two-sided shooting. The specific two-body Keplerian propagation method used by both of these models is described. Methods for incorporating realistic operational constraints and hardware models at the preliminary stage of a trajectory design effort are also demonstrated and the analytic methods derived are tested for accuracy using automatic differentiation. A companion paper will solve several relevant problems that show the utility of employing analytic derivatives, i.e. compared to using derivatives found using finite differences.