Modelling of very high voltage transmission lines inspection’s quadrotor

Abstract

In this study, we present a general mathematical model of a quadrotor unmanned aerial vehicle (UAV), that is dedicated to the transmission lines inspection. It takes into account the mechanical forces and torques, based on the quaternion approach to avoid the singularity problem, and the interference effects of the electromagnetic field, generated by the high voltages transmission lines, on the quadrotor. In order to establish a mathematical model that considers all the constraints of our mission type and to release a specific inspection transmission lines quadrotor, contrary to the mathematical models presented in most of the research works which are mechanical models that describe just a general flight case of a UAV. The choice of the quadcopter was made by comparing it with other methods of transmission lines inspection, as it is the cheapest, easiest, safest, and most efficient to meet our need. To express mechanical and electromagnetic equations and laws, we suppose that the quadrotor’s structure is rigid and symmetrical, the propellers are rigid, the center of mass and the origin of the body frame coincide, the lift and drag forces are proportional to the squares of the rotation speed of the rotors, the earth is a perfect conductor and the root-mean-square line voltages are constant.