Development of mathematical model of spatial flight of a kvadrokopter

Aeronautical engineering


Ogoltsov I. I.*, Rozhnin N. B.**, Sheval V. V.***

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia



The article discusses the physical and mathematical models of spatial flight unmanned aerial vehicle helicopter — type drone. These devices have received wide application in various fields of national economy. However, a deterrent to their wider use is the lack of a common approach to defining the shape of the autopilot, allowing purposefully and with acceptable quality to automatically control the flight path of the drone. The investigated materials are intended to define the shape of the autopilot, its structure, basic circuits and their parameters. The physical model of a kvadrokopter considering all main forces and the moments causing him forward and rotary motions is offered. On the presented physical model of the spatial movement of a kvadrokopter mathematical descriptions are developed. According to the presented physical model of the motion of a quadrocopter developed mathematical descriptions. They all control forces and moments are generated by using four Electromechanical DC motors with propellers on their rotors. Forces and moments are created independently by each engine by regulating its speed. In mathematical models the ineradicable interactions between various drives of traction screws having fairly complex character are considered. It is necessary to consider the spatial movement in all six degrees of freedom for more correct description of the motion of a quadrocopter . The peculiarity of the task to be solved was consideration of the dynamics of the actuators, forming the traction forces and moments with the screws. The main contours in the structure of the autopilot: contour stabilization of the angular position of the quadrocopter, the contour of the positioning of the quadrocopter in space and circuit for stabilizing the speed of rotation of the motors, that together purposefully to control the flight path and the angular position quadrocopters space. were considered in the course of research on mathematical models of the dynamics of the movement. Algorithms of realization the control in each of contours are offered. The Suggestions on selection of parameters of contours of control allowing to provide the steady movements of the acceptable quality are given. All offers formulated in work are checked by means of digital computing experiment. The received results allow to develop the autopilot for control of a kvadrokopter with the set characteristics of accuracy and stability.


quadrocopter, digital model of spatial movement, flight control, autopilot control loops


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  2. Ogol’tsov I.I., Rozhnin N.B., Sheval’ V.V. Materialy IX Vserossiiskoi nauchno-tekhnicheskoi konferentsii «Problemy sovershenstvovaniya robototekhnicheskikh i intellektual’nykh sistem letatel’nykh apparatov», Moscow, 2012, pp. 309-317.

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