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Efficient Computation of Optimal Low Thrust Gravity Perturbed Orbit Transfers

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Abstract

We have developed a new method for solving low-thrust fuel-optimal orbit transfer problems in the vicinity of a large body (planet or asteroid), considering a high-fidelity spherical harmonic gravity model. The algorithm is formulated via the indirect optimization method, leading to a two-point boundary value problem (TPBVP). We make use of a hyperbolic tangent smoothing law for performing continuation on the thrust magnitude to reduce the sharpness of the control switches in early iterations and thus promote convergence. The TPBVP is solved using the method of particular solutions (MPS) shooting method and Picard-Chebyshev numerical integration. Application of Picard-Chebyshev integration affords an avenue for increased efficiency that is not available with step-by-step integrators. We demonstrate that computing the particular solutions with only a low-fidelity force model greatly increases the efficiency of the algorithm while ultimately achieving near machine precision accuracy. A salient feature of the MPS is that it is parallelizable, and thus further speedups are available. It is also shown that, for near-Earth orbits and over a small number of en-route revolutions around the Earth, only the zonal perturbation terms are required in the costate equations to obtain a solution that is accurate to machine precision and optimal to engineering precision. The proposed framework can be used for trajectory design around small asteroids and also for orbit debris rendezvous and removal tasks.

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Acknowledgment

Initial work was conducted by Woollands as a post-doctoral researcher at Texas A&M where she was funded by AFOSR (Staci Williams) and AFRL (Alok Das). Woollands continued and completed this work at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration, and was funded by a Spontaneous Research and Technology Development Grant (Fred Hadaegh). Taheri and Junkins were funded by AFOSR (Staci Williams) and AFRL (Alok Das).

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  1. Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, 91109, USA

    Robyn Woollands

  2. Department of Aerospace Engineering, Texas A&M University, College Station, TX, 77843-3141, USA

    Robyn Woollands, Ehsan Taheri & John L. Junkins

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  1. Robyn Woollands
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Woollands, R., Taheri, E. & Junkins, J.L. Efficient Computation of Optimal Low Thrust Gravity Perturbed Orbit Transfers. J Astronaut Sci 67, 458–484 (2020). https://doi.org/10.1007/s40295-019-00152-9

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