Development and research of drone swarm control via methods borrowed from continuum mechanics
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.
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