IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v132y2007i3d10.1007_s10957-007-9166-4.html
   My bibliography  Save this article

Optimal Trajectories for Spacecraft Rendezvous

Author

Listed:
  • A. Miele

    (Rice University)

  • M. W. Weeks

    (NASA-Johnson Space Center)

  • M. Ciarcià

    (Rice University)

Abstract

The efficient execution of a rendezvous maneuver is an essential component of various types of space missions. This work describes the formulation and numerical investigation of the thrust function required to minimize the time or fuel required for the terminal phase of the rendezvous of two spacecraft. The particular rendezvous studied concerns a target spacecraft in a circular orbit and a chaser spacecraft with an initial separation distance and separation velocity in all three dimensions. First, the time-optimal rendezvous is investigated followed by the fuel-optimal rendezvous for three values of the max-thrust acceleration via the sequential gradient-restoration algorithm. Then, the time-optimal rendezvous for given fuel and the fuel-optimal rendezvous for given time are investigated. There are three controls, one determining the thrust magnitude and two determining the thrust direction in space. The time-optimal case results in a two-subarc solution: a max-thrust accelerating subarc followed by a max-thrust braking subarc. The fuel-optimal case results in a four-subarc solution: an initial coasting subarc, followed by a max-thrust braking subarc, followed by another coasting subarc, followed by another max-thrust braking subarc. The time-optimal case with fuel given and the fuel-optimal case with time given result in two, three, or four-subarc solutions depending on the performance index and the constraints. Regardless of the number of subarcs, the optimal thrust distribution requires the thrust magnitude to be at either the maximum value or zero. The coasting periods are finite in duration and their length increases as the time to rendezvous increases and/or as the max allowable thrust increases. Another finding is that, for the fuel-optimal rendezvous with the time unconstrained, the minimum fuel required is nearly constant and independent of the max available thrust. Yet another finding is that, depending on the performance index, constraints, and initial conditions, sometime the initial application of thrust must be delayed, resulting in an optimal rendezvous trajectory which starts with a coasting subarc.

Suggested Citation

  • A. Miele & M. W. Weeks & M. Ciarcià, 2007. "Optimal Trajectories for Spacecraft Rendezvous," Journal of Optimization Theory and Applications, Springer, vol. 132(3), pages 353-376, March.
    • Handle: RePEc:spr:joptap:v:132:y:2007:i:3:d:10.1007_s10957-007-9166-4
    DOI: 10.1007/s10957-007-9166-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-007-9166-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-007-9166-4?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. A. Miele & T. Wang, 2003. "Multiple-Subarc Gradient-Restoration Algorithm, Part 1: Algorithm Structure," Journal of Optimization Theory and Applications, Springer, vol. 116(1), pages 1-17, January.
    2. A. Miele & M. Ciarcià & M. W. Weeks, 2007. "Guidance Trajectories for Spacecraft Rendezvous," Journal of Optimization Theory and Applications, Springer, vol. 132(3), pages 377-400, March.
    3. A. Miele & T. Wang, 2003. "Multiple-Subarc Gradient-Restoration Algorithm, Part 2: Application to a Multistage Launch Vehicle Design," Journal of Optimization Theory and Applications, Springer, vol. 116(1), pages 19-39, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Y.-K. Chang & J. J. Nieto & W.-S. Li, 2009. "On Impulsive Hyperbolic Differential Inclusions with Nonlocal Initial Conditions," Journal of Optimization Theory and Applications, Springer, vol. 140(3), pages 431-442, March.
    2. Sandeep K. Singh & Brian D. Anderson & Ehsan Taheri & John L. Junkins, 2021. "Low-Thrust Transfers to Southern $$L_2$$ L 2 Near-Rectilinear Halo Orbits Facilitated by Invariant Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 191(2), pages 517-544, December.
    3. Fliege, Jörg & Kaparis, Konstantinos & Khosravi, Banafsheh, 2012. "Operations research in the space industry," European Journal of Operational Research, Elsevier, vol. 217(2), pages 233-240.
    4. A. Miele & M. Ciarcià, 2008. "Optimal Starting Conditions for the Rendezvous Maneuver, Part 1: Optimal Control Approach," Journal of Optimization Theory and Applications, Springer, vol. 137(3), pages 593-624, June.
    5. A. Miele & M. Ciarcià, 2008. "Optimal Starting Conditions for the Rendezvous Maneuver, Part 2: Mathematical Programming Approach," Journal of Optimization Theory and Applications, Springer, vol. 137(3), pages 625-639, June.
    6. A. Miele & M. Ciarcià & M. W. Weeks, 2007. "Guidance Trajectories for Spacecraft Rendezvous," Journal of Optimization Theory and Applications, Springer, vol. 132(3), pages 377-400, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. A. Miele & M. Ciarcià, 2008. "Optimal Starting Conditions for the Rendezvous Maneuver, Part 1: Optimal Control Approach," Journal of Optimization Theory and Applications, Springer, vol. 137(3), pages 593-624, June.
    2. A. Miele & T. Wang, 2005. "Maximin Approach to the Ship Collision Avoidance Problem via Multiple-Subarc Sequential Gradient-Restoration Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 124(1), pages 29-53, January.
    3. Mauro Pontani & Bruce Conway, 2014. "Optimal Low-Thrust Orbital Maneuvers via Indirect Swarming Method," Journal of Optimization Theory and Applications, Springer, vol. 162(1), pages 272-292, July.
    4. N. Yokoyama & S. Suzuki & T. Tsuchiya, 2008. "Convergence Acceleration of Direct Trajectory Optimization Using Novel Hessian Calculation Methods," Journal of Optimization Theory and Applications, Springer, vol. 136(3), pages 297-319, March.
    5. A. Miele & T. Wang & J. A. Mathwig & M. Ciarcià, 2010. "Collision Avoidance for an Aircraft in Abort Landing: Trajectory Optimization and Guidance," Journal of Optimization Theory and Applications, Springer, vol. 146(2), pages 233-254, August.
    6. A. Miele & T. Wang, 2006. "Optimal Trajectories and Guidance Schemes for Ship Collision Avoidance," Journal of Optimization Theory and Applications, Springer, vol. 129(1), pages 1-21, April.
    7. A. Miele & M. Ciarcià & M. W. Weeks, 2007. "Guidance Trajectories for Spacecraft Rendezvous," Journal of Optimization Theory and Applications, Springer, vol. 132(3), pages 377-400, March.
    8. A. Miele & M. Ciarcià, 2008. "Optimal Starting Conditions for the Rendezvous Maneuver, Part 2: Mathematical Programming Approach," Journal of Optimization Theory and Applications, Springer, vol. 137(3), pages 625-639, June.
    9. Y.-K. Chang & J. J. Nieto & W.-S. Li, 2009. "On Impulsive Hyperbolic Differential Inclusions with Nonlocal Initial Conditions," Journal of Optimization Theory and Applications, Springer, vol. 140(3), pages 431-442, March.
    10. A. Miele & T. Wang, 2003. "Multiple-Subarc Gradient-Restoration Algorithm, Part 1: Algorithm Structure," Journal of Optimization Theory and Applications, Springer, vol. 116(1), pages 1-17, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:132:y:2007:i:3:d:10.1007_s10957-007-9166-4. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.