Multirotor modelling and simulation: Screws, S.O.A., Euler angles, quaternions, wind

In this paper we present the modeling and simulation of multi-rotors using Spatial Operator Algebra. We develop two dynamic models one where the speeds are in the inertial frame and another where the speeds are vehicle frame. In both the reference point is the center of mass, but the method applies to any point of the vehicle. Besides gravity, the external forces considered include the effect of the propellers and the wind. The kinematic relationships between the angular speeds in the different frames are established using Euler angles and quaternions. Both models were programmed and the results presented, for a free flying quadcopter. When Euler angles are used to define the attitude we found that they are useful for a very limited range of angles. Quaternions do not have these limitations.