Time-Optimal Planning for Quadrotor Waypoint Flight

Quadrotors are amongst the most agile flying robots. However, planning
time-optimal trajectories at the actuation limit through multiple
waypoints remains an open problem. This is crucial for applications such
as inspection, delivery, search and rescue, and drone racing. Early works
used polynomial trajectory formulations, which do not exploit the full
actuator potential due to their inherent smoothness.  Recent
works resorted to numerical optimization, but require waypoints to be
allocated as costs or constraints at specific discrete times. However,
this time-allocation is a priori unknown and renders previous works
incapable of producing truly time-optimal trajectories. To generate truly
time-optimal trajectories, we propose a solution to the time allocation
problem while exploiting the full quadrotor's actuator potential. We
achieve this by introducing a formulation of progress along the
trajectory, which enables the simultaneous optimization of the
time-allocation and the trajectory itself. We compare our method against
related approaches and validate it in real-world flights in one of the
world's largest motion-capture systems, where we outperform human
expert drone pilots in a drone-racing task.