用学习模型加速无人机最优轨迹生成，实现实时飞行。
Sequence Modeling for Time-Optimal Quadrotor Trajectory Optimization with Sampling-based Robustness Analysis
- 用神经网络模仿基于模型的最优规划器，快速生成轨迹。
- 在未见过的路径长度上仍保持良好泛化能力。
- 通过随机扰动增强鲁棒性，适合真实无人机平台部署。
时间最优轨迹使四旋翼飞行器逼近其动态极限，但求解此类轨迹需通过迭代非线性优化，计算成本高，难以用于实时场景。本文研究基于学习的模型，模仿基于模型的时间最优轨迹规划器以加速轨迹生成。给定一组无碰撞的几何路径数据集，我们证明建模架构能有效学习时间最优轨迹的规律。引入定量分析框架，研究学习模型的局部解析性质，并将其与几何跟踪控制器的后向可达管（Backward Reachable Tube）关联。为提升鲁棒性，提出一种数据增强方法，在输入路径上施加随机扰动。相比传统规划器，本方法实现显著提速，并在硬件四旋翼平台上验证了实时可行性。实验表明，学习模型可泛化至此前未见的路径长度。代码见：https://github.com/maokat12/lbTOPPQuad。
原文摘要 · Abstract (English)
Time-optimal trajectories drive quadrotors to their dynamic limits, but computing such trajectories involves solving non-convex problems via iterative nonlinear optimization, making them prohibitively costly for real-time applications. In this work, we investigate learning-based models that imitate a model-based time-optimal trajectory planner to accelerate trajectory generation. Given a dataset of collision-free geometric paths, we show that modeling architectures can effectively learn the patterns underlying time-optimal trajectories. We introduce a quantitative framework to analyze local analytic properties of the learned models, and link them to the Backward Reachable Tube of the geometric tracking controller. To enhance robustness, we propose a data augmentation scheme that applies random perturbations to the input paths. Compared to classical planners, our method achieves substantial speedups, and we validate its real-time feasibility on a hardware quadrotor platform. Experiments demonstrate that the learned models generalize to previously unseen path lengths. The code for our approach can be found here: https://github.com/maokat12/lbTOPPQuad
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