  In this paper, we propose a novel data-driven approach for learning and
control of quadrotor UAVs based on the Koopman operator and extended dynamic
mode decomposition (EDMD). Building observables for EDMD based on conventional
methods like Euler angles (to represent orientation) is known to involve
singularities. To address this issue, we employ a set of physics-informed
observables based on the underlying topology of the nonlinear system. We use
rotation matrices to directly represent the orientation dynamics and obtain a
lifted linear representation of the nonlinear quadrotor dynamics in the SE(3)
manifold. This EDMD model leads to accurate prediction and can be generalized
to several validation sets. Further, we design a linear model predictive
controller (MPC) based on the proposed EDMD model to track agile reference
trajectories. Simulation results show that the proposed MPC controller can run
as fast as 100 Hz and is able to track arbitrary reference trajectories with
good accuracy. Implementation details can be found in
\url{https://github.com/sriram-2502/KoopmanMPC_Quadrotor}.
