  Quadrotors are extremely agile, so much in fact, that classic
first-principle-models come to their limits. Aerodynamic effects, while
insignificant at low speeds, become the dominant model defect during high
speeds or agile maneuvers. Accurate modeling is needed to design robust
high-performance control systems and enable flying close to the platform's
physical limits. We propose a hybrid approach fusing first principles and
learning to model quadrotors and their aerodynamic effects with unprecedented
accuracy. First principles fail to capture such aerodynamic effects, rendering
traditional approaches inaccurate when used for simulation or controller
tuning. Data-driven approaches try to capture aerodynamic effects with blackbox
modeling, such as neural networks; however, they struggle to robustly
generalize to arbitrary flight conditions. Our hybrid approach unifies and
outperforms both first-principles blade-element theory and learned residual
dynamics. It is evaluated in one of the world's largest motion-capture systems,
using autonomous-quadrotor-flight data at speeds up to 65km/h. The resulting
model captures the aerodynamic thrust, torques, and parasitic effects with
astonishing accuracy, outperforming existing models with 50% reduced prediction
errors, and shows strong generalization capabilities beyond the training set.

Robotics