  We consider the problem of generating a time-optimal quadrotor trajectory
that attains a set of prescribed waypoints. This problem is challenging since
the optimal trajectory is located on the boundary of the set of dynamically
feasible trajectories. This boundary is hard to model as it involves
limitations of the entire system, including hardware and software, in agile
high-speed flight. In this work, we propose a multi-fidelity Bayesian
optimization framework that models the feasibility constraints based on
analytical approximation, numerical simulation, and real-world flight
experiments. By combining evaluations at different fidelities, trajectory time
is optimized while keeping the number of required costly flight experiments to
a minimum. The algorithm is thoroughly evaluated in both simulation and
real-world flight experiments at speeds up to 11 m/s. Resulting trajectories
were found to be significantly faster than those obtained through minimum-snap
trajectory planning.
