TRAJECTORY OPTIMIZATION USING REGULARIZED VARIABLES

When the trajectory of a space vehicle passes through regions with significantly different gravitational force magnitudes, numerical accuracy requirements often necessitate extreme computer times. In celestial mechanics, regularizing transformations are used to eliminate computational and analytical problems that occur during close approaches to gravitational force centers. Based on results obtained in celestial mechanics studies, it can be expected that regularization in the formulation of the trajectory optimization problem may benefit the convergence characteristics as well as reduce the computation time. In this investigation, regularized equations for the optimal trajectory of a space vehicle with continuous thrust are obtained. The computational characteristics of the regularized equations are compared with the characteristics of the unregularized equations using a perturbation type numerical optimization method. The comparison is made for a three-dimensional, lowthrust, Earth-Jupiter rendezvous transfer. The comparison indicates that, when the regularized equations are used, a significant reduction in computing time is obtained. Furthermore, for the values considered in this study, the convergence of the regularized equations is much less sensitive to errors in the guesses for the unknown boundary conditions. © 1969 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.