Русская версия
ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

About History Editorial Page Addresses Scope Editorial Staff Submission Review For Authors Publication Ethics Issues Русская версия

On One Problem of Optimal Control of a Quadcopter with a Given Intermediate Value of Part of the Coordinates of the Phase Vector

Author(s):

Vanya Rafaelovich Barseghyan

Doctor of Physical and Mathematical Sciences, Professor. Leading Scientific Researcher of Institute of Mechanics of NAS of RA
Professor of Mathematics and Mechanics Department of Yerevan State University (YSU)

barseghyan@sci.am

Tamara Aleksanovna Simonyan

Candidate of Physical and Mathematical
Sciences, Associate Professor. Associate Professor of Mathematics and Mechanics
Department of Yerevan State University (YSU)

simtom09@gmail.com

Aram Gagikovich Matevosyan

Candidate of Physical and Mathematical
Sciences, Associate Professor. Associate Professor of Mathematics and Mechanics
Department of Yerevan State University (YSU)

amatevosyan@ysu.am

Abstract:

Taking into account the growing use of quadcopters for various purposes, this work is devoted to considering the issues of mathematical modeling of their spatial motion and constructing a program optimal control law that ensures flight with a given intermediate value of part of the coordinates of the phase vector at some point in time. Based on the laws of theoretical mechanics, a system of differential equations describing the spatial motion of the quadcopter is given. For a linearized mathematical model of the motion of a quadcopter and a quadratic functional, the problem of constructing an optimal control law with given initial and final values of the phase vector and the value of a part of the coordinates at an intermediate point in time solved by the method of problems of moments. Optimal control functions and corresponding phase trajectories of optimal motion are constructed, taking into account the value of a part of the coordinates at some intermediate point in time. To illustrate the proposed approach, explicit expressions for the program optimal control function, phase coordinates of motion and corresponding graphs are constructed for specific numerical values.

Keywords

References:

  1. Sitnikov D. V., Burian Y. A., Russkih G. S. Avtopilot mul'tikoptera [Motion Control System of Multicopter]. Proceedings Of the Tula States University. Technical sciences. 2012. № 7. P. 213-221(in Russ. )
  2. D. Т Rubin., V. N. Konev, А. V. Starikovsky, А. А. Sheptunov. Razrabotka kvadrokopterov so spetsial'nymi svoystvami dlya provedeniya razvedyvatel'nykh operatsiy [Development of special quadrocopters for survey works]. Spetstekhnika i svyaz - Special machinery and communications, 2012, No. 1(in Russ. )
  3. Epov M. I., Zlygostev I. N., Primeneniye bespilotnykh letatel'nykh apparatov v aerogeofizicheskoy razvedke [Application of unmanned aerial vehicles in airborne geophysical reconnaissance]. Sbornik materialov Interekspo GEO-Sibir, 2:3 (2012), 22-27 (In Russ)
  4. Telukhin S. V., Matveyev V. V. Bespilotnyy letatel'nyy apparat kak ob" yekt upravleniya [Unmanned aerial vehicle as an object of control. ]. Mekhatronika, avtomatizatsiya, upravleniye. 2008. № 10. 7-10. (in Russ. )
  5. Chettibi T., Haddad M. Dynamic modelling of a quadrotor aerial robot // Journees D’etudes Nationales de Mecanique. Batna, Algerie, 2007. P. 22-27
  6. Mokhtari A., Benallegue A. Dynamic feedback controller of Euler angles and wind parameters estimation for a quadrotor unmanned aerial vehicle // Proceedings - IEEE International Conference on Robotics and Automation. 2004. V. 2004. N 3. P. 2359-2366
  7. Derafa L., Madani T., Benallegue A. Dynamic modelling and experimental identification of four rotors helicopter parameters // Proceedings of the IEEE International Conference on Industrial Technology. 2006. Art. 4237837. P. 1834-1839
  8. Margun A. A., Zimenko K. A., Bazylev D. N., Bobtsov A. A., Kremlev A. S., Ibraev D. D. Sistema upravleniya bespilotnym letatel'nym apparatom, osnashchennym robototekhnicheskim manipulyatorom [Control System For Unmanned Aircraft Equipped With Robotics Arm]. Scientific and Technical Journal of Information Technologies, Mechanics and Optics" . 2014. №6 (94). P 54-62 (In Russ)
  9. Luukkonen T. Modelling and control of quadcopter. 2011. http://sal.aalto.fi/publications/pdf-files/eluu11_public.pdf
  10. Puls T., Hein A. 3D trajectory control for quadrocopter // Intelligent Robots and System (IROS), IEEE/RSJ International Conference. 2010. P. 640-645
  11. Benić Z., Piljek P. and Kotarski D. Mathematical modelling of unmanned aerial vehicles with four rotors. Interdisciplinary Description of Complex Systems. 2016. 14(1), pp. 88-100
  12. Ashchepkov, L. T., Optimal'noye upravleniye sistemoy s promezhutochnymi usloviyami [Optimal Control of a System with Intermediate Conditions], J. Appl. Math. Mech. , 1981, vol. 45, no. 2, pp. 153-158
  13. Dykhta V. A., Samsonyuk O. N. Printsip maksimuma dlya gladkikh zadach optimal'nogo impul'snogo upravleniya s mnogotochechnymi fazoogranicheniyami[The maximum principle for smooth problems of optimal impulse control with multipoint phase constraints]. Zhurnal vychislitel'noy matematiki i matematicheskoy fiziki. 2009, t. 49, № 6, s. 981-997. (in Russ. )
  14. Barseghyan, V. R. Upravlenie sostavnyh dinamicheskih sistem i sistem s mnogotochechnymi promezhutochnymi usloviyami. [Control of Compound Dynamic Systems and of Systems with Multipoint Intermediate Conditions]. M. : Nauka, 2016. (in Russ. )
  15. Barseghyan V. R. Control of stage by stage changing linear dynamic systems // Yugoslav Journal of Operations Resarch. 2012. Vol. 22. № 1. P. 31-39
  16. Barseghyan V. R. and Barseghyan T. V. On an Approach to the Problems of Control of Dynamic System with Nonseparated Multipoint Intermediate Conditions. Automation and Remote Control, 2015, Vol. 76, № 4, pp. 549-559
  17. Barseghyan V. R, Matevosyan A. G. On One Problem of Controlling an Airplane-type Unmanned Aerial Vehicle with Given Intermediate Values of Different Parts of Coordinates. Differential Equations and Control Processes, 2023, Issue 2, P. 86-96. St Petersburg State University
  18. Barseghyan V. R. Control Problem of String Vibrations with Inseparable Multipoint Conditions at Intermediate Points in Time. Mechanics of Solids. 2019. Vol. 54, Issue 8, pp. 1216-1226
  19. Barseghyan V., Solodusha S. On One Problem in Optimal Boundary Control for String Vibrations with a Given Velocity of Points at an Intermediate Moment of Time // IEEE International Russian Automation Conference (RusAutoCon). 2021. P. 343-349
  20. Krasovsky N. N. Teoriya upravleniya dvizheniem [The Theory of Motion Control]. M. : Nauka, 1968. (in Russ. )

Full text (pdf)