Over the past decade, there has been a remarkable surge in utilizing quadrotors for various purposes due to their simple structure and aggressive maneuverability, such as search and rescue, delivery and autonomous drone racing, etc. One of the key challenges preventing quadrotors from being widely used in these scenarios is online waypoint-constrained time-optimal trajectory generation and control technique. This letter proposes an imitation learning-based online solution to efficiently navigate the quadrotor through multiple waypoints with time-optimal performance. The neural networks (WN&CNets) are trained to learn the control law from the dataset generated by the time-consuming CPC algorithm and then deployed to generate the optimal control commands online to guide the quadrotors. To address the challenge of limited training data and the hover maneuver at the final waypoint, we propose a transition phase strategy that utilizes polynomials to help the quadrotor 'jump over' the stop-and-go maneuver when switching waypoints. Our method is demonstrated in both simulation and real-world experiments, achieving a maximum speed of 7 m/s while navigating through 7 waypoints in a confined space of 6.0 m * 4.0 m * 2.0 m. The results show that with a slight loss in optimality, the WN&CNets significantly reduce the processing time and enable online optimal control for multiple-waypoint-constrained flight tasks.

翻译：过去十年间，得益于其结构简单和强机动性，四旋翼飞行器在搜索救援、物流配送及自主无人机竞速等场景中得到广泛应用。制约其大规模应用的核心挑战之一，在于实现满足航点约束的在线时间最优轨迹生成与控制技术。本文提出一种基于模仿学习的在线解决方案，可高效引导四旋翼飞行器以时间最优性能穿越多个航点。通过训练神经网络（WN&CNets）学习由耗时CPC算法生成的数据集中的控制律，并将其部署于在线环境以生成最优控制指令。针对训练数据有限及末端航点悬停动作的难题，我们提出过渡阶段策略，在切换航点时利用多项式辅助飞行器"跨越"停-走动作。仿真与实物实验表明，该方法在6.0米×4.0米×2.0米受限空间内穿越7个航点时，最大速度可达7米/秒。结果显示，WN&CNets在牺牲轻微最优性的前提下，显著缩短处理时间，实现了多航点约束飞行任务的在线最优控制。