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.

翻译：流匹配（Flow Matching, FM）在数据驱动规划中已展现出显著成效。然而，该方法天然缺乏对状态约束与动作约束的形式化保证——满足这些约束是确保各类系统规划轨迹安全性与可容许性的基本且关键的要求。此外，现有流匹配规划器无法保证动态一致性，这可能导致轨迹不可执行。为克服上述缺陷，我们提出SAD-Flower——一种生成安全、可容许且动态一致轨迹的新型框架。该方法通过对流增广虚拟控制输入实现核心突破，进而利用非线性控制理论推导出基于原则的引导机制，为状态约束、动作约束及动态一致性提供形式化保证。关键在于，SAD-Flower无需重新训练即可运行，支持在测试阶段满足未见约束。通过跨多项任务的广泛实验，我们证明SAD-Flower在确保约束满足方面优于多种基于生成模型的基线方法。