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MATHEMATICAL MODELLING OF UNMANNED
AERIAL VEHICLES WITH FOUR ROTORS

Zoran Benić1,
Petar Piljek2 and
Denis Kotarski3

1Končar D&ST
Zagreb, Croatia

2Faculty of Mechanical Engineering and Naval Architecture - University of Zagreb
Zagreb, Croatia

3Karlovac University of Applied Sciences
Karlovac, Croatia

 INDECS 14(1), 88-100, 2016 DOI 10.7906/indecs.14.1.9 Full text available here. Received: 17 December 2015. Accepted: 20 January 2016. Regular article

ABSTRACT

Mathematical model of an unmanned aerial vehicle with four propulsors (quadcopter) is indispensable in quadcopter movement simulation and later modelling of the control algorithm. Mathematical model is, at the same time, the first step in comprehending the mathematical principles and physical laws which are applied to the quadcopter system. The objective is to define the mathematical model which will describe the quadcopter behavior with satisfactory accuracy and which can be, with certain modifications, applicable for the similar configurations of multirotor aerial vehicles. At the beginning of mathematical model derivation, coordinate systems are defined and explained. By using those coordinate systems, relations between parameters defined in the earth coordinate system and in the body coordinate system are defined. Further, the quadcopter kinematic is described which enables setting those relations. Also, quadcopter dynamics is used to introduce forces and torques to the model through usage of Newton-Euler method. Final derived equation is Newton's second law in the matrix notation. For the sake of model simplification, hybrid coordinate system is defined, and quadcopter dynamic equations derived with the respect to it. Those equations are implemented in the simulation. Results of behavior of quadcopter mathematical model are graphically shown for four cases. For each of the cases the propellers revolutions per minute (RPM) are set in a way that results in the occurrence of the controllable variables which causes one of four basic quadcopter movements in space.

KEY WORDS

quadcopter, earth frame, body frame, rotation matrix, Newton-Euler method, control variable

CLASSIFICATION

 JEL: Z19 PACS: 07.05.Tp, 87.19.Iu

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