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Low-Thrust Many-Revolution Trajectory Optimization via Differential Dynamic Programming and a Sundman Transformation

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Abstract

Low-thrust trajectories about planetary bodies characteristically span a high count of orbital revolutions. Directing the thrust vector over many revolutions presents a challenging optimization problem for any conventional strategy. This paper demonstrates the tractability of low-thrust trajectory optimization about planetary bodies by applying a Sundman transformation to change the independent variable of the spacecraft equations of motion to an orbit angle and performing the optimization with differential dynamic programming. Fuel-optimal geocentric transfers are computed with the transfer duration extended up to 2000 revolutions. The flexibility of the approach to higher fidelity dynamics is shown with Earth’s J2 perturbation and lunar gravity included for a 500 revolution transfer.

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Acknowledgments

This work was supported by a NASA Space Technology Research Fellowship. This work utilized the RMACC Summit supercomputer, which is supported by the National Science Foundation (awards ACI-1532235 and ACI-1532236), the University of Colorado Boulder, and Colorado State University. The Summit supercomputer is a joint effort of the University of Colorado Boulder and Colorado State University.

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Authors and Affiliations

  1. Colorado Center for Astrodynamics Research, University of Colorado, Boulder, CO, 80309, USA

    Jonathan D. Aziz

  2. Advanced Space, Boulder, CO, 80301, USA

    Jeffrey S. Parker

  3. Colorado Center for Astrodynamics Research, University of Colorado, Boulder, CO, 80309, USA

    Daniel J. Scheeres

  4. NASA/GSFC, Code 595, 8800 Greenbelt Rd, Greenbelt, MD, 20771, USA

    Jacob A. Englander

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  1. Jonathan D. Aziz
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  2. Jeffrey S. Parker
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  4. Jacob A. Englander
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Correspondence to Jonathan D. Aziz.

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Aziz, J.D., Parker, J.S., Scheeres, D.J. et al. Low-Thrust Many-Revolution Trajectory Optimization via Differential Dynamic Programming and a Sundman Transformation. J of Astronaut Sci 65, 205–228 (2018). https://doi.org/10.1007/s40295-017-0122-8

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  • DOI: https://doi.org/10.1007/s40295-017-0122-8

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