  We tackle the problem of flying time-optimal trajectories through multiple
waypoints with quadrotors. State-of-the-art solutions split the problem into a
planning task - where a global, time-optimal trajectory is generated - and a
control task - where this trajectory is accurately tracked. However, at the
current state, generating a time-optimal trajectory that considers the full
quadrotor model requires solving a difficult time allocation problem via
optimization, which is computationally demanding (in the order of minutes or
even hours). This is detrimental for replanning in presence of disturbances. We
overcome this issue by solving the time allocation problem and the control
problem concurrently via Model Predictive Contouring Control (MPCC). Our MPCC
optimally selects the future states of the platform at runtime, while
maximizing the progress along the reference path and minimizing the distance to
it. We show that, even when tracking simplified trajectories, the proposed MPCC
results in a path that approaches the true time-optimal one, and which can be
generated in real-time. We validate our approach in the real world, where we
show that our method outperforms both the current state-of-the-art and a
world-class human pilot in terms of lap time achieving speeds of up to 60 km/h.
