Abstract Variational approach to optimal control theory converts trajectory optimization problems into two- or multiple-point boundary-value problems, which consist of costates (i.e., Lagrange multipliers associated with the states). Estimating missing values of the non-intuitive costates is an important step in solving the resulting boundary-value problems. By leveraging costate vector mapping theorem, we extend the method of Adjoint Control Transformation (ACT), called Mapped ACT (MACT), to alternative sets of coordinates/elements for solving low-thrust trajectory optimization problems. In particular, extension of the ACT method to the set of modified equinoctial elements and an orbital element set based on the specific angular momentum and eccentricity vectors (h-e) is demonstrated. The computational and robustness efficiency of the MACT method is compared against the traditionally used random initialization of costates by solving 1) interplanetary rendezvous maneuvers and 2) an Earth-centered, orbit-raising problem with and without the inclusion of J 2 perturbation. For the considered problems, numerical results indicate two to three times improvement in the percent of convergence of the resulting boundary-value problems when the MACT method is used compared to the random initialization method. Results also indicate that the h-e set is also a contender and suitable choice for solving low-thrust trajectory optimization problems.

    Highlights Costate initialization of minimum-fuel low-thrust trajectory optimization problems is considered. The Adjoint Control Transformation (ACT) method is extended to other sets of coordinates/elements. Extensive numerical simulations are performed for interplanetary and planet-centric maneuvers. h-e element set is a suitable choice for solving low-thrust trajectory optimization problems. Two to three times improvement in percent of convergence of the boundary-value problems is possible.


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    Title :

    Mapped adjoint control transformation method for low-thrust trajectory design


    Contributors:

    Published in:

    Acta Astronautica ; 193 ; 418-431


    Publication date :

    2021-12-08


    Size :

    14 pages




    Type of media :

    Article (Journal)


    Type of material :

    Electronic Resource


    Language :

    English