DIDO (software)

DIDO is a fast optimal control toolbox for solving general-purpose optimal control problems.[1][2][3] Based on the pseudospectral optimal control theory of Ross and Fahroo,[4] the MATLAB optimal control toolbox is named after Dido, the legendary founder and first queen of Carthage who is famous in mathematics for her remarkable solution to a constrained optimal control problem even before the invention of calculus.

Theory

DIDO is based on pseudospectral optimal control theory founded by Ross and his associates.[2] The object-oriented software utilizes trademarked expressions and objects[1] that facilitate a user to quickly formulate and solve optimal control problems.[5][6][7] Rapidity in formulation is achieved through a set of DIDO expressions which are based on variables commonly used in optimal control theory.[1] The covector mapping principle of Ross and Fahroo eliminates traditional difficulties in solving for the costates in optimal control problems; thus, DIDO generates spectrally accurate solutions [8] whose extremality can be verified using Pontryagin's Minimum Principle.[1] Because no knowledge of pseudospectral methods is necessary to use DIDO, it is often used as a fundamental mathematical tool for solving optimal control problems. That is, a solution obtained from DIDO is treated as a candidate solution for the application of Pontryagin's minimum principle as a necessary condition for optimality.[1]

Applications

DIDO is used world wide in academia, industry and government laboratories.[9] Thanks to NASA, DIDO was flight-proven in 2006.[2] On November 5, 2006, NASA used DIDO to maneuver the International Space Station to perform the Zero Propellant Maneuver. The Zero Propellant Maneuver was discovered by Nazareth Bedrossian using DIDO. Watch a video of this historic maneuver.

Since this historic flight demonstration, DIDO has been used in operate the International Space Station and other NASA spacecraft.[10] It is also used in other industries to generate real-time optimal solutions.[1][9]

The youtube videos DIDO: Part 1 and DIDO: Part 2 show more applications and explain some of the new mathematics.

History

Invented by Ross, DIDO was first produced in 2001[6] and has many firsts to its credit:[4] [10] [11] [12] [13] [7] [14]

Versions

DIDO is a professional optimal control solver; however, several different versions of DIDO are available:

In addition the complete source code for DIDO is also available so that an end user may customize it for any application.

See also

References

  1. 1 2 3 4 5 6 Ross, I. M. A Primer on Pontryagin's Principle in Optimal Control, Second Edition, Collegiate Publishers, San Francisco, 2015.
  2. 1 2 3 Ross, I. M.; Karpenko, M. (2012). "A Review of Pseudospectral Optimal Control: From Theory to Flight". Annual Reviews in Control. 36: 182–197. doi:10.1016/j.arcontrol.2012.09.002.
  3. ↑ Ross, I. M.; D'Souza, C. N. (2005). "A Hybrid Optimal Control Framework for Mission Planning". Journal of Guidance, Control and Dynamics. 28 (4): 686–697. doi:10.2514/1.8285.
  4. 1 2 Ross, I. M.; Fahroo, F. (2004). "Pseudospectral Knotting Methods for Solving Optimal Control Problems". Journal of Guidance, Control and Dynamics. 27 (3): 397–405. doi:10.2514/1.3426.
  5. ↑ A. M. Hawkins, Constrained Trajectory Optimization of a Soft Lunar Landing From a Parking Orbit, S.M. Thesis, Dept. of Aeronautics and Astronautics, Massachusetts Institute of Technology, 2005. http://dspace.mit.edu/handle/1721.1/32431
  6. 1 2 J. R. Rea, A Legendre Pseudospectral Method for Rapid Optimization of Launch Vehicle Trajectories, S.M. Thesis, Dept. of Aeronautics and Astronautics, Massachusetts Institute of Technology, 2001. http://dspace.mit.edu/handle/1721.1/8608
  7. 1 2 Josselyn, S.; Ross, I. M. (2003). "A Rapid Verification Method for the Trajectory Optimization of Reentry Vehicles". Journal of Guidance, Control and Dynamics. 26 (3): 505–508. doi:10.2514/2.5074.
  8. ↑ Gong, Q.; Fahroo, F.; Ross, I. M. (2008). "A Spectral Algorithm for Pseudospectral Methods in Optimal Control". Journal of Guidance, Control and Dynamics. 31 (3): 460–471. doi:10.2514/1.32908.
  9. 1 2 Q. Gong, W. Kang, N. Bedrossian, F. Fahroo, P. Sekhavat and K. Bollino, Pseudospectral Optimal Control for Military and Industrial Applications, 46th IEEE Conference on Decision and Control, New Orleans, LA, pp. 4128-4142, Dec. 2007.
  10. 1 2 L. Keesey, "TRACE Spacecraft's New Slewing Procedure." NASA's Goddard Space Flight Center. National Aeronautics and Space Administration. Dec. 20, 2010. (Sept. 11, 2011) http://www.nasa.gov/mission_pages/sunearth/news/trace-slew.html.
  11. ↑ Fahroo, F.; Doman, D. B.; Ngo, A. D. (2003). "Modeling Issues in Footprint Generation of Resuable Launch Vehicles". Proceedings of the IEEE Aerospace Conference. 6: 2791–2799. doi:10.1109/aero.2003.1235205.
  12. ↑ W. Kang and N. Bedrossian, "Pseudospectral Optimal Control Theory Makes Debut Flight, Saves nasa $1m in Under Three Hours," SIAM News, 40, 2007.
  13. ↑ B. Honegger, "NPS Professor's Software Breakthrough Allows Zero-Propellant Maneuvers in Space." Navy.mil. United States Navy. April 20, 2007. (Sept. 11, 2011) http://www.elissarglobal.com/wp-content/uploads/2011/07/Navy_News.pdf.
  14. ↑ National Aeronautics and Space Administration. "Fact Sheet: International Space Station Zero-Propellant Maneuver (ZPM) Demonstration." June 10, 2011. (Sept. 13, 2011) http://www.nasa.gov/mission_pages/station/research/experiments/ZPM.html

Further reading

External links

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