DIDO (software) explained

DIDO is a MATLAB optimal control toolbox for solving general-purpose optimal control problems.[1] [2] [3] [4] It is widely used in academia, industry, and NASA.[5] Hailed as a breakthrough software,[6] DIDO is based on the pseudospectral optimal control theory of Ross and Fahroo.[7] The latest enhancements to DIDO are described in Ross.

Usage

DIDO utilizes trademarked expressions and objects that facilitate a user to quickly formulate and solve optimal control problems.[8] [9] Rapidity in formulation is achieved through a set of DIDO expressions which are based on variables commonly used in optimal control theory. For example, the state, control and time variables are formatted as:

The entire problem is codified using the key words, cost, dynamics, events and path:

A user runs DIDO using the one-line command:

[cost, primal, dual] = dido(problem, algorithm),

where the object defined by algorithm allows a user to choose various options. In addition to the cost value and the primal solution, DIDO automatically outputs all the dual variables that are necessary to verify and validate a computational solution. The output dual is computed by an application of the covector mapping principle.

Theory

DIDO implements a spectral algorithm based on pseudospectral optimal control theory founded by Ross and his associates.[10] The covector mapping principle of Ross and Fahroo eliminates the curse of sensitivity associated in solving for the costates in optimal control problems. DIDO generates spectrally accurate solutions [11] whose extremality can be verified using Pontryagin's Minimum Principle. Because no knowledge of pseudospectral methods is necessary to use it, DIDO 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.

Applications

DIDO is used world wide in academia, industry and government laboratories.[12] Thanks to NASA, DIDO was flight-proven in 2006. On November 5, 2006, NASA used DIDO to maneuver the International Space Station to perform the zero-propellant maneuver.

Since this flight demonstration, DIDO was used for the International Space Station and other NASA spacecraft.[13] [14] [15] [16] [17] [18] It is also used in other industries.[2] [12] Most recently, DIDO has been used to solve traveling salesman type problems in aerospace engineering.[19]

MATLAB optimal control toolbox

DIDO is primarily available as a stand-alone MATLAB optimal control toolbox.[20] That is, it does not require any third-party software like SNOPT or IPOPT or other nonlinear programming solvers. In fact, it does not even require the MATLAB Optimization Toolbox.

The MATLAB/DIDO toolbox does not require a "guess" to run the algorithm. This and other distinguishing features have made DIDO a popular tool to solve optimal control problems.

The MATLAB optimal control toolbox has been used to solve problems in aerospace, robotics and search theory.

History

The 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. Invented by Ross, DIDO was first produced in 2001.[21] The software is widely cited[22] [23] [24] [25] and has many firsts to its credit:[26] [27] [13] [28] [29] [30]

Versions

The early versions, widely adopted in academia,[31] have undergone significant changes since 2007. The latest version of DIDO, available from Elissar Global,[32] does not require a "guess" to start the problem[33] and eliminates much of the minutia of coding by simplifying the input-output structure. Low-cost student versions and discounted academic versions are also available from Elissar Global.

See also

Further reading

External links

Notes and References

  1. Enhancements to the DIDO Optimal Control Toolbox. Ross. Isaac. 2020. math.OC. 2004.13112.
  2. Ross, I. M. A Primer on Pontryagin's Principle in Optimal Control, Second Edition, Collegiate Publishers, San Francisco, 2015.
  3. Eren, H., "Optimal Control and the Software," Measurements, Instrumentation, and Sensors Handbook, Second Edition, CRC Press, 2014, pp.92-1-16.
  4. Ross . I. M. . I. Michael Ross . D'Souza . C. N. . 15828363 . 2005 . A Hybrid Optimal Control Framework for Mission Planning . Journal of Guidance, Control and Dynamics . 28 . 4. 686–697 . 10.2514/1.8285. 2005JGCD...28..686R .
  5. Web site: Steigerwald. Bill. 2021-02-10. Teaching an Old Spacecraft New Tricks to Continue Exploring the Moon. 2021-07-16. NASA.
  6. Book: Kallrath, Josef. Modeling Languages in Mathematical Optimization. Kluwer Academic Publishers. 2004. Dordrecht, The Netherlands. 379–403.
  7. Ross . I. M. . Fahroo . F. . 11140975 . 2004 . Pseudospectral Knotting Methods for Solving Optimal Control Problems . Journal of Guidance, Control and Dynamics . 27 . 3. 397–405 . 10.2514/1.3426.
  8. 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
  9. PhD. Infeld. Samantha I.. 2005. Optimization of Mission Design for Constrained Libration Point Space Missions. Stanford University. 2006PhDT.........7I.
  10. Ross . I. M. . Karpenko . M. . 2012 . A Review of Pseudospectral Optimal Control: From Theory to Flight . Annual Reviews in Control . 36 . 2. 182–197 . 10.1016/j.arcontrol.2012.09.002.
  11. Gong . Q. . Fariba Fahroo . I. Michael Ross . 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 . 10.2514/1.32908. 10945/56995 . 2008JGCD...31..460G . 18145691 . free .
  12. 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.
  13. 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.
  14. Web site: NASA Technical Reports Server (NTRS). 2020-12-24. ntrs.nasa.gov. 31 January 2019 .
  15. Karpenko. Mark. King. Jeffrey T.. Dennehy. Cornelius. J.. Michael Ross. I.. April 2019. Agility Analysis of the James Webb Space Telescope. Journal of Guidance, Control, and Dynamics. 42. 4. 810–821. 10.2514/1.g003816. 2019JGCD...42..810K . 126541985 . 0731-5090. 10945/63118. free.
  16. Karpenko, M. et al. "Fast Attitude Maneuvers for the Lunar Reconnaissance Orbiter." (2019) AAS 19-053.
  17. King. Jeffery T.. Karpenko. Mark. March 2016. A simple approach for predicting time-optimal slew capability. Acta Astronautica. 120. 159–170. 10.1016/j.actaastro.2015.12.009. 2016AcAau.120..159K . 111986660 . 0094-5765.
  18. Karpenko, M., Ross, I. M., Stoneking, E. T., Lebsock, K. L., Dennehy, C., "A Micro-Slew Concept for Precision Pointing of the Kepler Spacecraft," AAS 15-628.
  19. Book: Ross. I. M.. Proulx. R. J.. Karpenko. M.. 2019 American Control Conference (ACC) . Autonomous UAV Sensor Planning, Scheduling and Maneuvering: An Obstacle Engagement Technique . July 2019. http://dx.doi.org/10.23919/acc.2019.8814474. 65–70. IEEE. 10.23919/acc.2019.8814474. 978-1-5386-7926-5. 201811463 .
  20. Web site: DIDO: Optimal control software . Promotional web page . Mathworks .
  21. 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
  22. Book: Rao, A. V.. Optimization and Optimal Control in Automotive Systems . Trajectory Optimization: A Survey . 2014. LNCIS 455. 3–21. 10.1007/978-3-319-05371-4_1. Lecture Notes in Control and Information Sciences. 978-3-319-05370-7.
  23. Conway. B. A.. 2012. A Survey of Methods Available for the Numerical Optimization of Continuous Dynamical Systems. Journal of Optimization Theory and Applications. 152. 2. 271–306. 10.1007/s10957-011-9918-z. 10469414 .
  24. D. Delahaye, S. Puechmorel, P. Tsiotras, and E. Feron, "Mathematical Models for Aircraft Trajectory Design : A Survey" Lecture notes in Electrical Engineering, 2014, Lecture Notes in Electrical Engineering, 290 (Part V), pp 205-247
  25. S. E. Li, K. Deng, X. Zang, and Q. Zhang, "Pseudospectral Optimal Control of Constrained Nonlinear Systems," Ch 8, in Automotive Air Conditioning: Optimization, Control and Diagnosis, edited by Q. Zhang, S. E. Li and K. Deng, Springer 2016, pp. 145-166.
  26. National Aeronautics and Space Administration. "Fact Sheet: International Space Station Zero-Propellant Maneuver (ZPM) Demonstration." June 10, 2011. (Sept. 13, 2011) https://web.archive.org/web/20101107001300/http://www.nasa.gov/mission_pages/station/research/experiments/ZPM.html
  27. W. Kang and N. Bedrossian, "Pseudospectral Optimal Control Theory Makes Debut Flight, Saves nasa $1m in Under Three Hours," SIAM News, 40, 2007.
  28. 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 .
  29. Josselyn . S. . Ross . I. M. . 14256785 . 2003 . A Rapid Verification Method for the Trajectory Optimization of Reentry Vehicles . Journal of Guidance, Control and Dynamics . 26 . 3. 505–508 . 10.2514/2.5074. 2003JGCD...26..505J .
  30. Book: Fahroo . F. . Doman . D. B. . Ngo . A. D. . 2003 IEEE Aerospace Conference Proceedings (Cat. No.03TH8652) . Modeling issues in footprint generation for reusable vehicles . 2003 . 6 . 2791–2799 . 10.1109/aero.2003.1235205. 978-0-7803-7651-9 . 10945/41266 . 109035122 .
  31. Web site: MIT OpenCourseWare Aeronautics and Astronautics 16.323 Principles of Optimal Control, Spring 2006 Lecture Notes. 2021-04-20. dspace.mit.edu.
  32. Web site: Elissar Global . web site . distributes the software.
  33. Book: Ross. I. Michael. Gong. Qi. AIAA/AAS Astrodynamics Specialist Conference and Exhibit . Guess-Free Trajectory Optimization . 2008-06-15. http://dx.doi.org/10.2514/6.2008-6273. Reston, Virginia. American Institute of Aeronautics and Astronautics. 10.2514/6.2008-6273. 10945/29657 . 978-1-62410-001-7. 122759348 .

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