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
@article{arxiv.2506.13915,
title = {Sequence Modeling for Time-Optimal Quadrotor Trajectory Optimization with Sampling-based Robustness Analysis},
author = {Katherine Mao and Hongzhan Yu and Ruipeng Zhang and Igor Spasojevic and M Ani Hsieh and Sicun Gao and Vijay Kumar},
journal= {arXiv preprint arXiv:2506.13915},
year = {2025}
}