Analytical partial derivative calculation of the sims-flanagan transcription match point constraints

Donald H. Ellison, Jacob A. Englander, Martin T. Ozimek, Bruce A. Conway

Research output: Chapter in Book/Report/Conference proceedingConference contribution


The optimization of low-thrust spacecraft trajectories is a complex problem that lends itself to the use of direct method optimization techniques, rather than indirect, primarily due to their ability to converge to a feasible solution from a very poor initial guess. Many low-thrust trajectory optimizers make use of large-scale nonlinear programming packages to solve the parameter optimization problem resulting from the discrete transcription of a continuous optimal control problem. The most well-known of these tools is probably the Sparse Nonlinear OPTimizer (SNOPT). The algorithms of gradient-based optimization packages such as SNOPT's sequential quadratic programming technique rely on knowledge of the system Jacobian. While SNOPT is capable of calculating the Jacobian entries numerically using finite differencing, specifying these partial derivatives analytically results in more efficient solver performance. We present methods for the calculation of exact analytical expressions for the partial derivatives of the match point constraints of the "up-to-unit vector control" variant of the Sims-Flanagan transcription. These derivatives represent approximately 92% of the dense Jacobian entries for the Sims-Flanagan problem and their analytical specification significantly increases solver execution speed and improves solution quality.

Original languageEnglish (US)
Title of host publicationAdvances In The Astronautical Sciences
EditorsDonald L. Mackison, Ossama Abdelkhalik, Roby S. Wilson, Renato Zanetti
PublisherUnivelt Inc.
Number of pages20
ISBN (Electronic)9780877036111
StatePublished - Jan 1 2014
Event24th AAS/AIAA Space Flight Mechanics Meeting, 2014 - Mexico, United States
Duration: Jan 26 2014Jan 30 2014

Publication series

NameAdvances in the Astronautical Sciences
ISSN (Print)0065-3438


Other24th AAS/AIAA Space Flight Mechanics Meeting, 2014
CountryUnited States

ASJC Scopus subject areas

  • Aerospace Engineering
  • Space and Planetary Science

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