Aerospace Trajectory Optimization with SOCS

Aerospace Trajectory Optimization with SOCS

Welcome

This web site describes Fortran computer programs that use the Sparse Optimal Control Software (SOCS) object code library developed by The Boeing Company (www.boeing.com/phantom/socs/) to solve practical aerospace trajectory optimization problems. All applications were created using version 6.4.7 of SOCS.

SOCS is a direct transcription method that can be used to solve a variety of trajectory optimization problems using the following combination of numerical methods:

· collocation and implicit integration

· adaptive mesh refinement

· sparse nonlinear programming

Additional information about the mathematical techniques and numerical methods used in SOCS can be found in the book, “Practical Methods for Optimal Control Using Nonlinear Programming” by John. T. Betts, SIAM, 2001.

For proper interface with the SOCS library, the user must provide Fortran routines that perform the following tasks:

· main program that sets algorithm control parameters and calls the SOCS transcription/optimal control subroutine

· perform initialization related to scaling, lower and upper bounds, initial conditions, etc.

· evaluate the right-hand-side differential equations

· define and compute any point and path constraints

· display the optimal solution results

SOCS will use this information to automatically transcribe the user’s problem and perform the optimization.

PLEASE NOTE: these applications are available as Fortran source code and do not include the SOCS library. This library must be purchased from Boeing.

EXAMPLE APPLICATION

The following files are the main Fortran source code routines for the ballistic interplanetary trajectory optimization example.

Main program	ipto_socs.f
Initialization	odeinp.for
Equations of motion	oderhs.for
Point functions	odepf.for
Print routine	odeprt.for

Please contact David Eagle at cdeaglejr@yahoo.com to purchase the source code for any of these applications.

Last updated February 23, 2010.

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SOCS Applications

Interpolation of Tabular Data

Minimum Curvature Spline Interpolation of Monovariate Tabular Simulation Data

PDF document (mcs_mono.pdf) freeware (mcs_mono.zip)

Minimum Curvature Spline Interpolation of Bivariate Tabular Simulation Data

PDF document (mcs_bivar.pdf) freeware (mcs_bivar.zip)

Geocentric Maneuver Optimization

Low-Thrust LEO-to-GEO Trajectory Optimization (PDF document – leo2geo.pdf)

Single Maneuver, Finite-Burn Trajectory Optimization (PDF document – one burn_socs.pdf)

Two Maneuver, Finite-Burn Trajectory Optimization (PDF document – twoburn_socs.pdf)

Atmospheric Re-entry Trajectory Optimization (PDF document – entry.pdf)

Aero-assist Trajectory Optimization (PDF document – aeroassist.pdf)

Earth Orbit Rendezvous Trajectory Optimization (PDF document – elambert1.pdf)

Finite-Burn, Earth Orbit Rendezvous Trajectory Optimization (PDF document- elambert2.pdf)

Lunar Trajectory Optimization

Impulsive TLI Delta-V Optimization (PDF document – tli_socs.pdf)

Optimal Finite-burn Trans-Lunar Injection (PDF document – fb_lsocs.pdf)

Translunar TCM Delta-V Optimization (PDF document – lunar_tcm_socs.pdf)

Lunar Landing Trajectory Optimization (PDF document – lunland.pdf)

Lunar Ascent Trajectory Optimization (PDF document – lvsocs.pdf)

Interplanetary Trajectory Optimization

Optimal Earth Orbit-to-Interplanetary Injection (PDF document – hyper_socs.pdf)

Ballistic Interplanetary Trajectory Optimization (PDF document – ipto_socs.pdf)

Low-Thrust Interplanetary Trajectory Optimization (PDF document – ilt_socs.pdf)

Interplanetary Gravity-Assist Trajectory Optimization (PDF document – flyby_socs.pdf)

Earth Escape Trajectory Optimization (PDF document – escape.pdf)

Interplanetary TCM Optimization (PDF document – itcm_socs.pdf)

Technical Notes

SOCS Software Architecture (socs_doc1.pdf)

Modified Equinoctial Orbital Elements (mee.pdf)

ECI Equations of Vehicle Motion (ecieqms.pdf)

Mission Constraints and Trajectory Optimization (targeting.pdf)

Flight Path Equations of Motion (fpeqms.pdf)

Additional Information

“Practical Methods for Optimal Control and Estimation Using Nonlinear Programming, Second Edition”, John T. Betts, the Society for Industrial and Applied Mathematics, 2010.

“Optimal Low Thrust Trajectories to the Moon”, John T. Betts and Sven O. Erb, SIAM Journal on Applied Dynamical Systems, Vol. 2, No. 2, pp. 144-170, 2003.

“Optimal Interplanetary Orbit Transfers by Direct Transcription”, John T. Betts, The Journal of the Astronautical Sciences, Vol. 42, No. 3, July-September 1994, pp. 247-268.

“Using Sparse Nonlinear Programming to Compute Low Thrust Orbit Transfers”, John T. Betts, The Journal of the Astronautical Sciences, Vol. 41, No. 3, July-September 1993, pp. 349-371.

“Sparse Jacobian Updates in the Collocation Method for Optimal Control Problems”, John T. Betts, AIAA Journal of Guidance, Control and Dynamics, Vol. 13, No. 3, May-June 1990.

“Trajectory Optimization on a Parallel Processor”, John T. Betts and William P. Huffman, AIAA Journal of Guidance, Control and Dynamics, Vol. 14, No. 2, March-April 1991.

“Application of Sparse Nonlinear Programming to Trajectory Optimization”, John T. Betts and William P. Huffman, AIAA Journal of Guidance, Control and Dynamics, Vol. 15, No. 1, January-February 1992.

“Path-Constrained Trajectory Optimization Using Sparse Sequential Quadratic Programming”, John T. Betts and William P. Huffman, AIAA Journal of Guidance, Control and Dynamics, Vol. 16, No. 1, January-February 1993.

“Application of Direct Transcription to Commercial Aircraft Trajectory Optimization”, John T. Betts and Evin J. Cramer, AIAA Journal of Guidance, Control and Dynamics, Vol. 18, No. 1, January-February 1995.

“Survey of Numerical Methods for Trajectory Optimization”, John T. Betts, AIAA Journal of Guidance, Control and Dynamics, Vol. 21, No. 2, March-April 1998.

cdeaglejr@yahoo.com www.cdeagle.com