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 takes the full quadrotor model into account 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-optimal planning and control problems 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.

翻译：我们通过带梯度的多条路点解决飞行时间最佳轨迹的问题。 最先进的解决方案将问题分为一个规划任务 — — 即产生全球、时间最优轨迹的地方 — — 和控制任务 — — 以及准确跟踪该轨迹的地方。 然而,在目前状态下,产生一个将全四极模型考虑在内的时间最优轨迹是计算性要求(按分钟或甚至小时顺序排列 ) 。 这不利于在出现扰动时重新规划。 我们通过模型预测跟踪控制(MPCC)同时解决时间最优的规划和控制问题来解决这一问题。 我们的MPCC在运行时最佳地选择平台的未来状态,同时尽量扩大参照路径上的进展并尽可能缩小其距离。 我们表明,即使跟踪简化轨迹时,拟议的多极轨迹也会导致一条接近真正时间最优的路径,并且可以实时生成。 我们验证了我们在现实世界中采用的方法, 在那里我们展示了我们的方法在运行时段上超越了60公里的时程速度, 从而实现了当前世界的飞行速度。