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

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 $\textbf{S}$afe, $\textbf{A}$dmissible, and $\textbf{D}$ynamically 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. Video and demos can be found at [sadflowerplanning.github.io](https://sadflowerplanning.github.io/project_web/).

Robots increasingly use generative AI to plan complex movements, such as navigating around obstacles, walking, or manipulating objects. However, these plans can be unsafe or impossible to execute: a generated trajectory may pass through an obstacle, ask the robot to use actions beyond its limits, or describe motion that does not follow the robot’s physics. We propose SAD-Flower, a method that adds a corrective steering mechanism to the generation process. Instead of retraining the generative model whenever new safety rules appear, SAD-Flower adjusts the generated trajectory at test time so that it respects safety limits, action limits, and the robot’s dynamics. The method does this by treating trajectory generation like a controllable system and solving small optimization problems during sampling. Across navigation, locomotion, and manipulation, SAD-Flower consistently satisfies the required constraints while maintaining competitive task performance. This work is a step toward generative planning methods that are not only flexible, but also more reliable for real-world robotic systems.