Quadrotors are among 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 because of 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.

Quadrotors 是最敏捷的飞行机器人之一。然而，通过多个航路点在致动极限处规划时间最优轨迹仍然是一个悬而未决的问题。这对于检查、交付、搜索和救援以及无人机竞赛等应用至关重要。早期的工作使用多项式轨迹公式，由于其固有的平滑性，它没有充分利用执行器的潜力。最近的工作求助于数值优化，但需要在特定的离散时间将航点分配为成本或约束。然而，这个时间分配是先验未知的，并且使之前的工作无法产生真正的时间最优轨迹。为了生成真正的时间最优轨迹，我们提出了一种解决时间分配问题的方法，同时利用了完整的四旋翼执行器的潜力。我们通过引入沿轨迹的进度公式来实现这一点，这可以同时优化时间分配和轨迹本身。我们将我们的方法与相关方法进行比较，并在世界上最大的动作捕捉系统之一的真实世界飞行中对其进行验证，在该系统中，我们在无人机竞赛任务中的表现优于人类专家无人机飞行员。