Quadrotor Dynamics in a Wind Field: Equilibria Analysis and Energy Dissipation

A widely used quadrotor model for designing controllers is based on rigid body dynamics, and it does not include the influence of wind, leading to several limitations. Namely, the quadrotor does not tilt when undergoing uniform linear motion; and it is not possible to account for energy dissipation due to wind and drag. To solve these two issues, we have added two types of aerodynamic drag due to wind into the quadrotor dynamics: propeller drag, and body drag. We conducted equilibria analyses of this model and observed that bifurcation occurs as the quadrotor body size is diminished. Through simulation, it was revealed that the model we propose overcomes the limitations of the rigid body model. Additionally, it has been demonstrated that the model we propose enables the calculation of energy dissipation due to wind, and the energy dissipation varies depending on the wind field distribution, even if the quadrotor's trajectory is the same. This metric can serve as a cost function for a new path-finding problem, aiding in the more efficient operation of quadrotors.