  Accurately modeling quadrotor's system dynamics is critical for guaranteeing
agile, safe, and stable navigation. The model needs to capture the system
behavior in multiple flight regimes and operating conditions, including those
producing highly nonlinear effects such as aerodynamic forces and torques,
rotor interactions, or possible system configuration modifications. Classical
approaches rely on handcrafted models and struggle to generalize and scale to
capture these effects. In this paper, we present a novel Physics-Inspired
Temporal Convolutional Network (PI-TCN) approach to learning quadrotor's system
dynamics purely from robot experience. Our approach combines the expressive
power of sparse temporal convolutions and dense feed-forward connections to
make accurate system predictions. In addition, physics constraints are embedded
in the training process to facilitate the network's generalization capabilities
to data outside the training distribution. Finally, we design a model
predictive control approach that incorporates the learned dynamics for accurate
closed-loop trajectory tracking fully exploiting the learned model predictions
in a receding horizon fashion. Experimental results demonstrate that our
approach accurately extracts the structure of the quadrotor's dynamics from
data, capturing effects that would remain hidden to classical approaches. To
the best of our knowledge, this is the first time physics-inspired deep
learning is successfully applied to temporal convolutional networks and to the
system identification task, while concurrently enabling predictive control.
