Mathematical modeling and control of a hexacopter

Microcopters are emerging as a popular platform for Unmanned Aerial Vehicle (UAV). The purpose of this paper is to present the basic mathematical modeling of microcopters, which has been used to develop proper methods for stabilization and trajectory control. The microcopter taken into account consists of six rotors, with three pairs of counter-rotating fixedpitch blades. The microcopter is controlled by adjusting the angular velocities of the rotors which are spun by electric motors. It is assumed as a rigid body, so the differential equations of the microcopter dynamics can be derived from both the Newton-Euler and Euler-Lagrange equations. Euler-angle parametrization of three-dimensional rotations contains singular points in the coordinate space that can cause failure of both dynamical model and control. In order to avoid singularities, the rotations of the microcopter are parametrized in terms of quaternions. This choice has been made taking into consideration the linearity of quaternion formulation, their stability and efficiency.