Provably Safe Motion Planning Under Unknown Disturbances

2026-05-26

AI Summary

This work addresses the problem of safe motion planning for robots operating in complex, cluttered environments under stochastic disturbances with unknown distributions. The authors propose a sampling-based, provably safe planning algorithm that constructs Wasserstein ambiguity tubes from trajectory data to tightly envelop the evolution of state distributions with high confidence. Building upon these tubes, the method incrementally grows a planning tree that satisfies chance constraints. A key innovation lies in replacing a single high-dimensional ambiguity tube with multiple lower-dimensional ones, substantially reducing conservatism and improving scalability. Additionally, an efficient, probabilistically complete bandit-style validity checker is introduced. Experimental results demonstrate that the approach reliably generates feasible trajectories meeting stringent safety thresholds in highly cluttered scenarios, significantly outperforming state-of-the-art methods.

Abstract

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.

Problem

• motion planning
• unknown disturbances
• chance-constraints
• safety
• robotic systems

Innovation

• Wasserstein ambiguity tube
• chance-constrained motion planning
• probabilistically complete sampling-based planning
• unknown disturbance
• bandit-based validity checker