Reachability-based Trajectory Design (RTD) is a provably safe, real-time trajectory planning framework that combines offline reachable-set computation with online trajectory optimization. However, standard RTD implementations suffer from two key limitations: conservatism induced by worst-case reachable-set overapproximations, and an inability to account for real-time disturbances during execution. This paper presents RTD-RAX, a runtime-assurance extension of RTD that utilizes a non-conservative RTD formulation to rapidly generate goal-directed candidate trajectories, and utilizes mixed monotone reachability for fast, disturbance-aware online safety certification. When proposed trajectories fail safety certification under real-time uncertainty, a repair procedure finds nearby safe trajectories that preserve progress toward the goal while guaranteeing safety under real-time disturbances.
@article{arxiv.2603.21635,
title = {RTD-RAX: Fast, Safe Trajectory Planning for Systems under Unknown Disturbances},
author = {Evanns Morales-Cuadrado and Long Kiu Chung and Shreyas Kousik and Samuel Coogan},
journal= {arXiv preprint arXiv:2603.21635},
year = {2026}
}