Development and research of drone swarm control via methods borrowed from continuum mechanics
Authors: Shchipanov M.A., Medvedev V.S.
Published in issue: #8(92)/2019
DOI: 10.18698/2308-6033-2019-8-1906
Category: Mechanics | Chapter: Mechanics of Deformable Solid Body
For a drone swarm in the form of a linear chain, there was solved a problem of maintaining the initially specified shape throughout the entire time of movement. To build a mathematical model of the drone chain, we applied the theory of movable cellular automata. By increasing the amount of elements in the chain, we obtained equations of oscillations of the chain in the longitudinal and transverse directions, similar to the equations of the longitudinal oscillations of the rod and the transverse oscillations of the tensioned string. We studied the longitudinal and transverse oscillations of the resulting system, resulting from the external disturbances, as well as the influence of these oscillations on the stability. Oscillation damping has been introduced, both in the longitudinal and transverse directions. Findings of research show that if damping is not introduced, it is not possible to maintain the drone formation using this method, i.e. the instability of the swarm motion process is emphasized. This problem is solved by introducing damping in the longitudinal and transverse directions, with damping in the longitudinal direction playing an important role.
References
[1] Floreano D., Wood R.J. Science, technology and the future of small autonomous drones. Nature, 2015, vol. 521, pp. 460–466.
[2] Turgut A.E., Ҫelikkanat H., Gӧkҫe F., Şahin E. Self-organized flocking in mobile robot swarms. Swarm intell., 2008, no. 2, pp. 97–120.
[3] Helbing D., Farkas I., Vicsek T. Simulating dynamical features of escape panic. Nature, 2000, vol. 407, pp. 487–490.
[4] Psakhie S.G, Smolin A.Yu., Dmitriev A.I., Shilko E.V., Korostelev S.Yu. Chebyshevskiy sbornik (Chebyshev collected papers), no. 18 (3), 2017, pp. 439–460. DOI: 10.22405/2226-8383-2017-18-3-439-460
[5] Herrmann H.J. Simulating granular media on the computer. 3rd Granada lectures in computational physics. P.L. Garrido, J. Marro, eds. Heidelberg, Springer, 1995, pp. 67–114.
[6] Levin V.A., ed. Nelineinaya vychislitelnaya mekhanika prochnosti. Tom 1. Modeli i metody. Obrazovanie i razvitie defektov [Nonlinear computational mechanics of strength. Vol. 1. Models and methods. Formation and development of defects]. Moscow, Fizmatlit Publ., 2015, 454 p.
[7] Levin V.A., Vershinin A.V. Nelineinaya vychislitelnaya mekhanika prochnosti. Tom 3. Chislennye metody. Realizatsiya na vysokoproizvoditelnykh vychislitelnykh sistemakh [Nonlinear computational mechanics of strength. Vol. 3. Numerical methods. Implementation on high-performance computing systems]. Moscow, Fizmatlit Publ., 2015, 543 p.
[8] Dobrynin S.A. Razvitie metoda podvizhnykh kletochnykh avtomatov dlya modelirovaniya generatsii i rasprostraneniya uprugikh voln pri kontaktnom vzaimodeistvii tverdykh tel. Diss. … kand. fiz.-mat. nauk [Development of the method of movable cellular automata for modeling the generation and propagation of elastic waves in the contact interaction of solids. Cand. Phys.-Math. Sc. Diss.]. Tomsk, 2010, 130 p.
[9] Dobrynin S.A. Kompyuternoe modelirovanie metodom podvizhnykh kletochnykh avtomatov [Computer simulation by the method of movable cellular automata]. Saarbrucken Germany: LAP LAMBERT Academic Publishing, 132 p. ISBN 978-3-8443-5954-1
[10] Goldshtein R.V., Gorodtsov V.A. Mekhanika sploshnykh sred. Chast 1 [Continuum mechanics. Part 1]. Moscow, Nauka Fizmatlit Publ., 2000, 256 p.
[11] Weaver W. Jr., Timoshenko S.P., Young D.H. Vibration problems in engineering. John Wiley & Sons, 1989, 620 p. [In Russ.: Timoshenko S.P., Young D.H. Kolebaniya v inzhenernom dele. Moscow, Mashinostroenie Publ., 1985, 472 p.].