Non-linear Mathematical Model of a Quad-Tiltrotor UAV Spatial Motion

Abstract

The article presents a design scheme of a quad-tiltrotor unmanned aerial vehicle (UAV), which combines a safe vertical take-off and landing procedures and a relatively large flight range inherent in the aircraft. In order to reduce the cost and weight of the quad-tiltrotor UAV, to increase its reliability, a circuit with minimization of movable executive drives is considered. Namely, in the proposed structural scheme of the quad-tiltrotor UAV there are no deflectable airfoils. In addition, the rotors of all four engines are rotated by the same setting angle in the longitudinal plane using a single actuator. The research results showed that the quadtiltrotor UAV of the proposed scheme as a whole is statically controlled. All the necessary balancing forces and moments are formed independently of each other only by a coordinated change in engine speed and control of the overall setting angle of their thrust vectors. It is also shown that there is a so-called degenerate flight mode in which static controllability is not provided. Theoretically, this is reflected in the degeneracy of the linear equation system matrix for determining the balance values of engine thrusts. Physically, the specified mode corresponds to the case when the resulting thrust vector of the engines lies on a straight line passing through the centre of gravity of the aircraft, and therefore it cannot create a pitch moment. The paper proposes two ways to overcome this limitation. The constructive method offers a special arrangement of rotor bushings. The algorithmic method carries out a quick transition through a degenerate balancing mode using a control system.