Modeling Quadrotor Dynamics in a Wind Field

This article presents aerodynamic modeling of quadrotors taking into account the effect of wind. Model equations are derived using blade element momentum theory and combined with classical quadrotor dynamics. Parameters are identified by a wind tunnel experiment. The resulting dynamics differ from the classical ones in two aspects. First, the effect of external wind is directly included. Second, the drag force and torque generated due to the movement of quadrotor itself, which exists without external wind, are also included. The second takes place because four propellers move in the air due to translational and rotational motions of the quadrotor. Both aspects are novel to the widely used quadrotor dynamics. Model validation is carried out by both theoretical analysis and experiment. Analyzing the model leads to the fact that when the quadrotor is linear-quadratic regulator controlled, it loses stability when wind amplitude exceeds a threshold. This fact has been experimentally validated using 20 different cases of wind amplitudes and directions. The experimental results well agree with the theoretical prediction.