Six-degree-of-freedom trajectory optimization using a two-timescale collocation architecture

Prasun N. Desai, Bruce A. Conway

Research output: Contribution to journalArticlepeer-review


Six-degree-of-freedom trajectory optimization of a reentry vehicle is performed using a two-timescale collocation methodology. This class of six-degree-of-freedom trajectory problems is characterized by two distinct timescales in their governing equations, in which a subset of the states have high-frequency dynamics (the rotational equations of motion), whereas the remaining states (the translational equations of motion) vary comparatively slowly. With conventional collocation methods, the six-degree-of-freedom problem becomes extraordinarily large and the problem becomes difficult to solve. Using the two-timescale collocation architecture, the problem size is reduced significantly. The converged solution shows a realistic landing profile and captures the appropriate high-frequency rotational dynamics. A large reduction in the overall problem size (by 55%) is attained with the two-timescale architecture as compared to the conventional single-timescale collocation method. Consequently, optimum sixdegree-of-freedom trajectories can now be found efficiently using collocation, which was not previously possible for a system with two distinct timescales in the governing states.

Original languageEnglish (US)
Pages (from-to)1308-1315
Number of pages8
JournalJournal of Guidance, Control, and Dynamics
Issue number5
StatePublished - 2008

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Aerospace Engineering
  • Space and Planetary Science
  • Electrical and Electronic Engineering
  • Applied Mathematics


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