SAD-Flower: Flow Matching for Safe, Admissible, and Dynamically Consistent Planning

TL;DR

SAD-Flower introduces a flow matching framework that guarantees safe, admissible, and dynamically consistent trajectories for planning, leveraging control theory to ensure formal constraint satisfaction without retraining.

Contribution

It proposes a novel augmentation of flow matching with virtual control inputs, providing formal guarantees for constraints and dynamic consistency in planning.

Findings

Outperforms baselines in constraint satisfaction

Ensures safety and admissibility without retraining

Demonstrates effectiveness across multiple tasks

Abstract

Flow matching (FM) has shown promising results in data-driven planning. However, it inherently lacks formal guarantees for ensuring state and action constraints, whose satisfaction is a fundamental and crucial requirement for the safety and admissibility of planned trajectories on various systems. Moreover, existing FM planners do not ensure the dynamical consistency, which potentially renders trajectories inexecutable. We address these shortcomings by proposing SAD-Flower, a novel framework for generating Safe, Admissible, and Dynamically consistent trajectories. Our approach relies on an augmentation of the flow with a virtual control input. Thereby, principled guidance can be derived using techniques from nonlinear control theory, providing formal guarantees for state constraints, action constraints, and dynamic consistency. Crucially, SAD-Flower operates without retraining, enabling test-time satisfaction of unseen constraints. Through extensive experiments across several tasks, we demonstrate that SAD-Flower outperforms various generative-model-based baselines in ensuring constraint satisfaction.