arXiv 2606.038342026-07-09cs.RO

让动力学流动：稳定的流匹配动力系统

Let the Dynamics Flow: Stable Flow Matching Dynamical Systems

Department of Robotics, Perception, and Learning, KTH Royal Institute of Technology（机器人、感知与学习系，皇家理工学院）；Advanced Mining Technology Center (AMTC) and Department of Electrical Engineering, Universidad de Chile（先进采矿技术中心（AMTC）和电气工程系，智利大学）；Bosch Center for Artificial Intelligence, Renningen, Germany（博世人工智能中心，德国Renningen）；Italian Institute of Artificial Intelligence (AI4I), Turin, Italy（意大利人工智能研究所（AI4I），意大利都灵）

Rodrigo Pérez-Dattari, Francisco Leiva, Andrea Testa, Leonel Rozo, Javier Ruiz del Solar, Noémie Jaquier

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AI总结：

提出稳定流匹配动力系统（SFMDS）框架，通过流匹配参数化动力系统并施加李雅普诺夫稳定性约束，实现稳定、可扩展、多模态的机器人运动生成。

摘要：

流匹配最近已成为模仿学习的一种强大方法，能够实现可扩展、表达力强且多模态的运动策略。然而，将这些生成模型纳入形式化的稳定性保证（确保机器人行为安全和可泛化的前提）仍然是一个重大挑战。虽然将机器人运动建模为动力系统允许这种基于稳定性的归纳偏置，但现有框架难以捕捉复杂机器人任务中固有的丰富动作分布。本文介绍了稳定流匹配动力系统（SFMDS），这是一个弥合高容量生成模型与形式化李雅普诺夫稳定性保证之间差距的新框架。SFMDS通过流匹配参数化动力系统，同时将模型约束到稳定解族。我们提出了两种变体：基于惩罚项的软约束，以及直接嵌入模型架构的硬结构约束。我们还将两种公式扩展到李群。在基准数据集、仿真和类人机器人上的实验表明，SFMDS在低维和高维状态空间中学习稳定、可扩展和多模态的动力系统，从而实现安全且富有表现力的机器人运动生成。

英文摘要：

Flow matching has recently emerged as a powerful approach for imitation learning, enabling scalable, expressive, and multimodal motion policies. However, when modeling these policies as dynamical systems, incorporating formal stability guarantees into these generative models is a prerequisite to ensure safe and generalizable robot behaviors, which remains a significant challenge. This paper introduces Stable Flow Matching Dynamical Systems (SFMDS), a novel framework that bridges the gap between highly expressive generative modeling and formal stability guarantees. SFMDS parametrizes dynamical systems via flow matching while constraining the model to satisfy positive invariance and/or Lyapunov stability conditions. We propose two variants: a soft constraint based on a penalty term, and a hard structural constraint embedded directly into the model architecture. We further extend both formulations to Lie groups to robustly handle orientation trajectories. Experiments on benchmark datasets, in simulation, and on a humanoid robot show that SFMDS learns stable, scalable, and multimodal dynamical systems in low- and high-dimensional state spaces, enabling safe and expressive robot motion generation. SFMDS matches or outperforms state-of-the-art methods on unimodal datasets, while substantially improving performance on multimodal datasets, where competing approaches fail to capture multi-modal behaviors. Accompanying source code and video are available at: https://let-the-dynamics-flow.github.io/SFMDS/.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。