Gaussian process models for preliminary low-thrust trajectory optimization

Lieve Bouwman, Yuxin Liu, Kevin Cowan

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientific

1 Citation (Scopus)
43 Downloads (Pure)


Low-thrust trajectories can benefit the search for propellant-optimal trajectories, but increases in modeling complexity and computational load remain a challenge for efficient mission design and optimization. In this paper, an approach for developing models utilizing Gaussian Process (GP) regression and classification is proposed to perform computationally efficient optimization while obtaining acceptable accuracies for trajectories based on exponential sinusoid shaping. The goal of this work is to predict a combination of values of input variables which corresponds to a shape-based trajectory with the smallest total velocity increment (ΔV) or propellant mass fraction (J m). A GP classification model is constructed to assess whether a given combination of values of input variables corresponds to a feasible trajectory. GP regression models are developed to predict the total ΔV and J m corresponding to a combination of shape parameters, which can replace the required integration along the shape. In addition, advanced regression models are developed to predict the target values while requiring only three input parameters, thereby replacing the entire shape computation. In order to develop a GP model that fits the problem at hand, the underlying functions and parameters should be selected rationally. In this work, a novel model development approach is proposed to ensure that the mean function, covariance function, likelihood function, inference method, and hyperparameters, which dominate the performance of the models, are chosen rationally in terms of mean absolute percentage error (MAPE) and prediction time. Using this approach, GP models are developed and tested on transfer trajectories from Earth to Mars and Ceres, and from Mars to Earth, and their performance, in terms of MAPE and prediction time, is compared to that of more common optimization techniques in combination with the exponential sinusoid and other shape-based methods. The results demonstrate that the computation time can significantly be reduced while achieving promising MAPE’s, especially when the goal is to locate regions of feasible or near-optimal trajectories. The proposed model development procedure is tested for robustness, which provides confidence in the proposed approach. Furthermore, it is found that the models which map three input variables directly to a ΔV or J m value perform better than the ones trained with shape information, which demonstrates the strength of GP models as applied to low-thrust trajectory optimization.

Original languageEnglish
Title of host publicationAAS/AIAA Astrodynamics Specialist Conference, 2019
EditorsKenneth R. Horneman, Christopher Scott, Brian W. Hansen, Islam I. Hussein
Number of pages20
ISBN (Electronic)978-0-87703-666-1
Publication statusPublished - 2020
Event2019 AAS/AIAA Astrodynamics Specialist Conference - Portland, United States
Duration: 11 Aug 201915 Aug 2019

Publication series

NameAdvances in the Astronautical Sciences
ISSN (Print)0065-3438


Conference2019 AAS/AIAA Astrodynamics Specialist Conference
Country/TerritoryUnited States

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.


Dive into the research topics of 'Gaussian process models for preliminary low-thrust trajectory optimization'. Together they form a unique fingerprint.

Cite this