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

Evanns Morales-Cuadrado; Long Kiu Chung; Shreyas Kousik; Samuel Coogan

cs.ROMar 23, 2026

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

Authors: Evanns Morales-Cuadrado, Long Kiu Chung, Shreyas Kousik, Samuel Coogan

Organizations: S. Coogan is also with the School of Civil and Environmental Engineering.

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.

Figures & tables

Figure 1: Narrow-gap scenario; the robot is depicted as a circle in the starting position, goal as a star, obstacles as rectangles, the offline reachable set in green, and the online reachable set in blue. (a) Standard RTD: incorrectly classifies as infeasible. (b) RTD-RAX : feasible and certified safe by the mixed-monotone verifier.

Figure 2: RTD-RAX architecture.

Panel of Figure 3 — Figure 3: Figures for the Narrow Gap scenario on the left and Angled Obstacle scenario on the right.

Figure 4: Disturbance-aware scenario. Left: standard RTD collides due to disturbances. Right: RTD-RAX with online certification accounts for disturbances and repairs unsafe candidates.

Pipeline Step	Standard RTD (ms)	RTD-RAX (ms)
Constraint setup	$2.15\pm 0.31$	$2.41\pm 0.22$
RTD solve	$6.48\pm 0.38$	$0.54\pm 0.04$
Reference rollout	$0.73\pm 0.17$	$1.22\pm 0.10$
immrax verify	$0$	$2.23\pm 0.14$
Repair loop	$0$	$4.20\pm 0.28$
Total cycle	$\mathbf{9.39\pm 0.56}$	$\mathbf{10.63\pm 0.72}$

Table 1: Case Study 3: Mean and standard deviation per planning cycle over 20 trials.

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Safe motion planning develops methods for robots and vehicles to reach goals while avoiding collisions and respecting dynamic and uncertainty constraints.

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We present a provably safe sampling-based motion planning algorithm for robotic systems affected by random disturbances of unknown distribution. We consider systems with linear or linearizable dynamics evolving in workspace with arbitrary-shaped obstacles subject to state and control constraints. Safety requirements are formulated as chance-constraints. Our approach leverages data from trajectories of the system to learn a Wasserstein ambiguity tube, i.e., a sequence of ambiguity sets, which contains the trajectory of the system's state distribution with high confidence. This ambiguity tube is then used in a probabilistically complete algorithm to grow a sampling-based motion planning tree that respects the constraints of the problem. We show that learning several lower-dimensional ambiguity tubes instead of a single high-dimensional one effectively reduces the conservatism and boosts scalability. Additionally, we design an efficient bandit-based validity checker that remarkably increases the empirical performance of our approach without sacrificing probabilistic completeness. Case studies show our algorithm finds valid plans in cluttered environments under strict safety thresholds, outperforming state-of-the-art methods.

Abstract

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