Fast and Robust Visuomotor Riemannian Flow Matching Policy

TL;DR

This paper presents RFMP, a fast, robust visuomotor policy leveraging flow matching on Riemannian manifolds, improving training speed, inference efficiency, and stability for complex robotic tasks.

Contribution

Introduction of RFMP and SRFMP, combining flow matching with geometric constraints and stability principles for improved robotic policy learning.

Findings

RFMP outperforms diffusion and consistency policies in various tasks.

RFMP enables efficient training and fast inference in high-dimensional spaces.

SRFMP enhances robustness through stability guarantees.

Abstract

Diffusion-based visuomotor policies excel at learning complex robotic tasks by effectively combining visual data with high-dimensional, multi-modal action distributions. However, diffusion models often suffer from slow inference due to costly denoising processes or require complex sequential training arising from recent distilling approaches. This paper introduces Riemannian Flow Matching Policy (RFMP), a model that inherits the easy training and fast inference capabilities of flow matching (FM). Moreover, RFMP inherently incorporates geometric constraints commonly found in realistic robotic applications, as the robot state resides on a Riemannian manifold. To enhance the robustness of RFMP, we propose Stable RFMP (SRFMP), which leverages LaSalle's invariance principle to equip the dynamics of FM with stability to the support of a target Riemannian distribution. Rigorous evaluation on ten simulated and real-world tasks show that RFMP successfully learns and synthesizes complex sensorimotor policies on Euclidean and Riemannian spaces with efficient training and inference phases, outperforming Diffusion Policies and Consistency Policies.