RTD-RAX: Fast, Safe Trajectory Planning for Systems under Unknown Disturbances

TL;DR

RTD-RAX enhances real-time trajectory planning by reducing conservatism and incorporating disturbance awareness, enabling fast, safe, goal-directed navigation in uncertain environments.

Contribution

It introduces a non-conservative RTD formulation and mixed monotone reachability for disturbance-aware safety certification, improving upon standard RTD methods.

Findings

Rapid generation of goal-directed trajectories

Fast online safety certification under disturbances

Effective repair of unsafe trajectories to ensure safety

Abstract

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.