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

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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 ΔV 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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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.

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Authors and Affiliations

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

    Sandeep K. Singh, John L. Junkins & Manoranjan Majji

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

    Ehsan Taheri

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  1. Sandeep K. Singh
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Correspondence to Sandeep K. Singh.

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Declaration of competing interest

The authors have no competing interests to declare that are relevant to the content of this article.

Sandeep K. Singh recently defended his Ph.D. in the Department of Aerospace Engineering at Texas A&M University, USA, under the guidance of Dr. John L. Junkins. He has worked as a graduate research fellow at NASA Jet Propulsion Laboratory, California Institute of Technology, USA, during the summer of 2019 and 2020. His current research interests include advanced optimal control methods, high-fidelity trajectory design, quasi-frozen orbits around irregular bodies and planets, and use of AI/ML techniques in mission design and other multi-disciplinary optimization problems. He will start in his new role as an assistant professor in the Department of Mechanical, Aerospace and Nuclear Engineering at Rensselaer Polytechnic Institute, USA in August 2022.

John L. Junkins is a professor at University Distinguished of Aerospace Engineering and a holder of the Royce E. Wisenbaker Chair in Innovation at Texas A&M University, USA. He is the founding director of the Hagler Institute for Advanced Study, USA. He was recently an interim president of Texas A&M University for 6 months ending in June 2021. He is a prolific scholar and has advised to completion 55 Ph.D. students. He is the author of over four-hundred papers and seven widely used technical books. His co-authored Analytical Mechanics of Aerospace Systems is now in its 4th edition and won the 2014 Martin Summerfield Best Book Award, given annually by AIAA. He is a member of the National Academy of Engineering, the National Academy of Inventors, the International Academy of Astronautics, and an Honorary Fellow of the American Institute for Aeronautics and Astronautics (AIAA), USA. He recently received the highest honor in his field, the AIAA Robert H. Goddard Astronautics Award (2019).

Manoranjan Majji is an associate professor of aerospace engineering and is the director of the Land, Air and Space Robotics (LASR) Laboratory at Texas A&M University, USA. He has a diverse background in several aspects of dynamics and control of aerospace vehicles with expertise spanning the whole spectrum of modeling, analysis, computations, and experiments. In the areas of state estimation, astrodynamics, tensegrity structures, and system identification, he has made fundamental contributions. He is a senior member of the IEEE, an associate fellow of the AIAA, and a fellow of the AAS.

Ehsan Taheri is an assistant professor at the Department of Aerospace Engineering in Auburn University, USA. His research focused on develo** dependable algorithms for solving optimal control problems associated with complex dynamical systems, including spacecraft equipped with low-thrust electric propulsion systems, entry, decent and landing vehicles, and multi-rotor unmanned aerial vehicles.

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Singh, S.K., Junkins, J.L., Majji, M. et al. Rapid accessibility evaluation for ballistic lunar capture via manifolds: A Gaussian process regression application. Astrodyn 6, 375–397 (2022). https://doi.org/10.1007/s42064-021-0130-0

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