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.

翻译：我们通过带梯子的多条路口解决飞行最优时间轨迹的问题。 最先进的解决方案将问题分为一个规划任务 — — 即产生一个全球最优时间轨迹的地方 — — 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,产生一个考虑到整个四极轨迹模型的最优时间轨迹,要求通过优化解决一个困难的时间分配问题,这是计算上的要求(按分钟或甚至小时顺序排列 ) 。这不利于在出现动乱时进行再规划。 我们通过模拟预测重叠控制(MPCC)同时解决时间分配问题和控制问题。 我们的MPCC在运行时最佳地选择平台的未来状态,同时尽可能扩大参照路径上的进展,并尽可能缩小其距离。 我们显示,即使跟踪简化轨迹,拟议的多极轨迹将带来一条通往真正最理想的路径,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, 也就是以60公里速度显示我们的方法超越了世界。