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

2025-11-07

AI Summary

Existing flow matching (FM)-based planning methods lack formal guarantees regarding state and action constraints, as well as dynamical consistency, resulting in unsafe, infeasible, or physically unrealizable trajectories. To address this, we propose SAD-Flower—a novel FM framework that, for the first time, integrates nonlinear control theory into the FM architecture. By introducing virtual control inputs, SAD-Flower enables explicit modeling of hard constraints while ensuring dynamic consistency throughout trajectory generation. Crucially, it supports zero-shot generalization to previously unseen constraints at test time without retraining. Evaluated across multiple robotic planning tasks, SAD-Flower significantly outperforms generative baselines: constraint satisfaction rates improve markedly, while generated trajectories remain provably safe, dynamically feasible, and physically executable.

Technology Category

• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Humans and AI: Human-Aware Planning and Behavior Prediction
• Intelligent Robots: Motion and Path Planning

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

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.

Problem

• Ensuring state and action constraint satisfaction in flow matching planning
• Addressing dynamical consistency for executable planned trajectories
• Providing formal safety guarantees without requiring model retraining

Innovation

• Uses virtual control input for flow augmentation
• Applies nonlinear control theory for formal guarantees
• Achieves constraint satisfaction without retraining