Quadrotor group control by variation analytical programming technique

Dynamics, ballistics, movement control of flying vehicles


Аuthors

Diveev A. I.1*, Konyrbaev N. B.2**

1. Federal Research Center “Computer Science and Control” of Russian Academy of Sciences, 44-2, Vavilova str., Moscow, 119333, Russia
2. Peoples' Friendship University of Russia, 6, Mikluho-Maklaya str., Moscow, 117198, Russia

*e-mail: aidiveev@mail.ru
**e-mail: n.konyrbaev@mail.ru

Abstract

The article analyzes an applied problem of area monitoring with a quadrotor group. The problem solves in two stages. At the first stage, the problem of searching an optimal route for each quadrotor is solving. This problem is the problem for travelling salesman group in 3D space, and related to the class of computation tasks of NP-difficulty. Variation genetic algorithm is applicable for such task solving. This genetic algorithm employs the principle small variations of basic solution. All genetic operations perform on the sets of basic solution variations. The rate of convergence of the genetic algorithm depends on the obtained basic solution. At the second stage, the problem of synthesis of quadrotors control to ensure their movement along the routs obtained at the first stage is solving. To solve the problem synthesis of control the numerical symbolic regression method was employed, i. e. method of variation analytical programming, which allows finding mathematical expression for a control function. The arguments of this function are contained in the quadrotor state vector. The control function ensures an optimal mode of quadrotor stability relative to the point in state space.

An example of control problem solution for two quadrotors group is presented.

Keywords:

control system synthesis, method of variation analytical programming, a flying robot, routing task for group of quadrotors

References

  1. Lubentsova E.V., Lubentsov V.F. Analiticheskoe konstruirovanie optimal’nykh regulyatorov (Analytical design of optimum regulators: manual), Stavropol’, Izd-vo Severo-Kavkazskogo federal’nogo universiteta, 2015, 114 p.

  2. Pomazueva E.A. Trudy MAI, 2015, no. 83, available at: http://trudymai.ru/eng/published.php?ID=623283

  3. Nemychenkov G.I. Trudy MAI, 2016, no. 89, available at: http://trudymai.ru/eng/published.php?ID=73376

  4. Kondrat’ev G.V. Geometricheskaya teoriya sinteza optimal’nykh statsionarnykh gladkikh sistem upravleniya (Geometrical theory of optimum stationary smooth control systems synthesis), Moscow, Nauka. Fizmatlit, 2003, 144 p.

  5. Matyushin M.M., Lutsenko Yu.S., Gershman K.E. Trudy MAI, 2016, no. 89, available at: http://trudymai.ru/eng/published.php?ID=72869

  6. Koza J.R. Genetic Programming: On the Programming of Computers by Means of Natural Selection. Cambridge, Massachusetts, London, MA: MIT Press, 1992, 819 p.

  7. Diveev A.I. Priblizhennye metody resheniya zadachi sinteza optimal’nogo upravleniya (Approximate methods of solution a problem of optimum control synthesis), Moscow, Izd-vo VTs RAN, 2015, 184 p.

  8. Diveev A.I. Izvestiya RAN. Teoriya i sistemy upravleniya, 2012, no. 2, pp. 63-78.

  9. Zelinka I. Analytic programming by Means of SOMA Algorithm. In Proceedings of 8th International Conference on Soft Computing Mendel’02, Brno, Czech Republic, 2002, pp. 93-101.

  10. Diveev A.I., Konyrbaev N.B. Sovremennye problemy nauki i obrazovaniya, 2014, no. 2, available at: https://science-education.ru/ru/article/view?id=12401

  11. Diveev A.I., Konyrbaev N.B. Fundamental’nye issledovaniya, 2015, no. 3, pp. 51–57.

  12. Diveev A.I., Ibadulla S.I., Konyrbaev N.B., Shmalko E.Yu. Variational Analytic Programming for Synthesis of Optimal Control for Flying Robot/ A.I. Diveev, S.I. Ibadulla, N.B. Konyrbaev, E.Yu Shmalko// Preprints of the 11th IFAC Symposium on Robot Control, Salvador, BA, Brazil, August 26-28, 2015, pp. 82-87.

  13. Diveev A.I., Konyrbaev N.B. Naukoemkie tekhnologii, 2015, vol. 16, no. 2, pp. 47-52.

  14. Diveev A.I., Konyrbaev N.B., Sofronova E.A. Method of binary analytic programming to look for optimal mathematical expression. XIIth International Symposium “Intelligent Systems”, INTELS’16, Moscow, 5-7 October 2016, pp. 597 – 604.

  15. Moiseev D.V., Chin’ V.M., Mozolev L.A., Moiseeva S.G., Fam S.K. Trudy MAI, 2015, no. 79, available at: http://trudymai.ru/eng/published.php?ID=55782

  16. Guerrero J., Lozano R. Flight Formation Control, London, John Wiley & Sons, 2012, 342 p.


Download

mai.ru — informational site MAI

Copyright © 2000-2021 by MAI

Вход