Low-Thrust Trajectory Design Optimization with Stochastic Convolution

Abstract

In this paper, a new stochastic based method for low-thrust trajectory design optimization is proposed. Indirect optimization methods based on optimal control theory (OCT) provide accurate solutions but convergence is difficult. In our new approach, an augmented Gaussian is used to relax the terminal conditions of the Two Point Boundary Value Problem (TPBVP), and model overall impacts of initial guess of costates. Objective function of the low-thrust trajectory design is transformed into a quasi-quadratic problem using quadratic convolution technique. The quasi-quadratic form objective function contains information matrix of the impacts due to varied costates and terminal conditions. A gradient based searching algorithm is then used to search the optimal initial guess. Based on the method, two algorithms are developed for resolving the TPBVP of low thrust trajectory design. Convergence performances of the algorithms are demonstrated through two low-thrust interplanetary trajectory design problems. Possible extension of the algorithm to multi-objective evolutionary optimization is also discussed.