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Trajectory Design Combining Invariant Manifolds with Discrete Mechanics and Optimal Control

Moore, Ashley and Blöbaum, Sina-Ober and Marsden, Jerrold E. (2012) Trajectory Design Combining Invariant Manifolds with Discrete Mechanics and Optimal Control. Journal of Guidance Control and Dynamics, 35 (5). pp. 1507-1525. ISSN 0731-5090. doi:10.2514/1.55426.

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A mission design technique that combines invariant manifold techniques, discrete mechanics, and optimal control produces locally optimal low-energy trajectories. Previously, invariant manifolds of the planar circular restricted three-body problem have been used to design trajectories with relatively small midcourse change in velocity ΔV. A different method of using invariant manifolds is explored to design trajectories directly in the four-body problem. Then, using the local optimal control method DMOC (Discrete Mechanics and Optimal Control), it is possible to reduce the midcourse ΔV to zero. The influence of different boundary conditions on the optimal trajectory is also demonstrated. These methods are tested on a trajectory that begins in Earth orbit and ends in ballistic capture at the moon. Impulsive DMOC trajectories require up to 19% less ΔV than trajectories using a Hohmann transfer. When applied to low-thrust trajectories, DMOC produces an improvement of up to 59% in the mass fraction and 22% in travel time when compared with results from shooting methods.

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Additional Information:© 2012 by the American Institute of Aeronautics and Astronautics, Inc. Received 9 July 2011; accepted for publication 13 February 2012. This work was generously supported in part by the National Defense Science and Engineering Graduate Fellowship, the W. M. Keck Institute for Space Studies, and the Collaborative Research Centre 614 “Self-Optimizing Concepts and Structures in Mechanical Engineering” funded by the German Research Foundation (Deutsche Forschungsgemeinschaft) under grant SFB 614.
Group:Keck Institute for Space Studies
Funding AgencyGrant Number
National Defense Science and Engineering Graduate FellowshipUNSPECIFIED
W. M. Keck Institute for Space StudiesUNSPECIFIED
Collaborative Research Centre 614UNSPECIFIED
German Research Foundation (DFG)SFB 614
Issue or Number:5
Record Number:CaltechAUTHORS:20130301-105652530
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Official Citation: Ashley Moore, Sina Ober-Blöbaum, and Jerrold E. Marsden. "Trajectory Design Combining Invariant Manifolds with Discrete Mechanics and Optimal Control", Journal of Guidance, Control, and Dynamics, Vol. 35, No. 5 (2012), pp. 1507-1525. doi: 10.2514/1.55426
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:37240
Deposited By: Ruth Sustaita
Deposited On:01 Mar 2013 19:17
Last Modified:09 Nov 2021 23:27

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