Co-states initialization of minimum-time low-thrust trajectories using shape-based methods

Abstract

This paper presents an approach for co-state initialization which is a crucial step in solving minimum-time low-thrust trajectory optimization problems using indirect optimal control numerical methods. Indirect methods used in determining the optimal space trajectories result in two-point boundary value problems which are typically solved by single- or multiple-shooting methods. Accurate initialization of the so-called co-state variables is necessary to achieve numerical convergence of iterative boundary value problem solvers. In this paper, we propose a method which exploits the trajectory generated by a shape-based method to estimate the initial values of the co-states. The performance of the algorithm is compared against two other approaches which respectively exploit random initialization of the co-states and a genetic algorithm. It is shown that by using the proposed approach, numerical convergence is improved especially for trajectories with higher number of revolutions.