Rapid accessibility evaluation for ballistic lunar capture via manifolds: A Gaussian process regression application

Sandeep K. Singh; John L. Junkins; Manoranjan Majji; Ehsan Taheri

doi:10.1007/s42064-021-0130-0

Astrodynamics 2022, 6(4): 375-397 https://doi.org/10.1007/s42064-021-0130-0

Research Article | Issue | Published: 19 April 2022

Rapid accessibility evaluation for ballistic lunar capture via manifolds: A Gaussian process regression application

Show Author's Information Hide Author's Information Sandeep K. Singh^¹(

), John L. Junkins^¹, Manoranjan Majji^¹, Ehsan Taheri^²

Department of Aerospace Engineering, Texas A&M University, College Station, TX 77843, USA

Department of Aerospace Engineering, Auburn University, Auburn, AL 36849, USA

Keywords:

supervised learning, Bayesian inference, invariant manifolds, Gaussian process regression, ballistic transfers

Cite this article:

Singh SK, Junkins JL, Majji M, et al. Rapid accessibility evaluation for ballistic lunar capture via manifolds: A Gaussian process regression application. Astrodynamics, 2022, 6(4): 375-397. https://doi.org/10.1007/s42064-021-0130-0

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Abstract

In this study, a supervised machine learning approach called Gaussian process regression (GPR) was applied to approximate optimal bi-impulse rendezvous maneuvers in the cis-lunar space. We demonstrate the use of the GPR approximation of the optimal bi-impulse transfer to patch points associated with various invariant manifolds in the cis-lunar space. The proposed method advances preliminary mission design operations by avoiding the computational costs associated with repeated solutions of the optimal bi-impulsive Lambert transfer because the learned map is computationally efficient. This approach promises to be useful for aiding in preliminary mission design. The use of invariant manifolds as part of the transfer trajectory design offers unique features for reducing propellant consumption while facilitating the solution of trajectory optimization problems. Long ballistic capture coasts are also very attractive for mission guidance, navigation, and control robustness. A multi-input single-output GPR model is presented to represent the fuel costs (in terms of the $Δ V$ magnitude) associated with the class of orbital transfers of interest efficiently. The developed model is also proven to provide efficient approximations. The multi-resolution use of local GPRs over smaller sub-domains and their use for constructing a global GPR model are also demonstrated. One of the unique features of GPRs is that they provide an estimate of the quality of approximations in the form of covariance, which is proven to provide statistical consistency with the optimal trajectories generated through the approximation process. The numerical results demonstrate our basis for optimism for the utility of the proposed method.

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Rapid accessibility evaluation for ballistic lunar capture via manifolds: A Gaussian process regression application

Show Author's information Hide Author's Information Sandeep K. Singh^¹(

), John L. Junkins^¹, Manoranjan Majji^¹, Ehsan Taheri^²

Department of Aerospace Engineering, Texas A&M University, College Station, TX 77843, USA

Department of Aerospace Engineering, Auburn University, Auburn, AL 36849, USA

Abstract

Keywords: supervised learning, Bayesian inference, invariant manifolds, Gaussian process regression, ballistic transfers

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Publication history

Acknowledgements

Publication history

Received: 02 November 2021

Accepted: 09 December 2021

Published: 19 April 2022

Issue date: December 2022

Copyright

Acknowledgements

We are pleased to acknowledge the Air Force Research Laboratory, Dzyne, Inc. and Texas A & M University for the sponsorship of various aspects of this research.