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Aerospace Trajectory Optimization Using Direct Transcription and Collocation

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Aerospace Trajectory Optimization Using Direct Transcription and Collocation


David Eagle (view profile)


06 Nov 2012 (Updated )

Demonstrates the solution of an aerospace trajectory optimization problem.

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In the language of optimal control theory, this problem is a “continuous system with functions of the state variables prescribed at a fixed terminal time”. The numerical example given in the text is a continuous, low-thrust coplanar orbit transfer from Earth to Mars. The orbits of the planets are assumed to be circular and coplanar, and the total transfer time is about 193 days.

MATLAB release MATLAB 8.0 (R2012b)
Other requirements This MATLAB script uses the SNOPT nonlinear programming algorithm to solve this trajectory optimization problem. MATLAB versions of SNOPT can be found at Professor Philip Gill’s web site which is located at
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Comments and Ratings (1)
15 Jul 2014 Nathan Parrish

Great walkthrough of direct transcription and collocation with a nice, simple example. Thanks!

24 Jun 2013 1.1

Updated PDF document and several m-files. Now includes graphic display of the heliocentric planet orbits and transfer trajectory. PDF document includes new dimensional analysis section, trajectory diagram, etc.

09 Sep 2013 1.2

Spelling correction of the title

07 Jul 2014 1.3

Added main script (dto_trap_64bit.m) that uses the March 17, 2014 version of SNOPT.

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