We consider the problem of generating a time-optimal quadrotor trajectory for highly maneuverable vehicles, such as quadrotor aircraft. The problem is challenging because 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 complex aerodynamic and electromechanical phenomena, 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 the number of costly flight experiments is kept to a minimum. The algorithm is thoroughly evaluated for the trajectory generation problem in two different scenarios: (1) connecting predetermined waypoints; (2) planning in obstacle-rich environments. For each scenario, we conduct 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.

我们考虑为高度机动的飞行器（例如四旋翼飞机）生成时间最佳四旋翼飞行轨迹的问题。该问题具有挑战性，因为最佳轨迹位于动态可行轨迹集的边界上。这个边界很难建模，因为它涉及整个系统的局限性，包括在敏捷高速飞行中复杂的空气动力学和机电现象。在这项工作中，我们提出了一个多保真贝叶斯优化框架，该框架基于解析近似、数值模拟和真实世界的飞行实验对可行性约束进行建模。通过结合不同保真度的评估，优化轨迹时间，同时将昂贵的飞行实验次数保持在最低限度。该算法针对两种不同场景下的轨迹生成问题进行了全面评估：（1）连接预定的航路点；(2) 在障碍物丰富的环境中进行规划。对于每个场景，我们都以高达 11 m/s 的速度进行模拟和真实世界的飞行实验。结果发现的轨迹比通过最小捕捉轨迹规划获得的轨迹要快得多。