Frequency-Aware Flow Matching for Continuous and Consistent Robotic Action Generation

2026-06-18

AI Summary

This work addresses limitations in existing flow-matching-based robotic motion generation methods, which rely on discrete action chunks and struggle with heterogeneous control frequencies in demonstration data, often yielding temporally inconsistent motions. The authors propose Frequency-Aware Flow Matching (FAFM), the first approach to integrate frequency-domain modeling with Sobolev-type constraints. FAFM maps actions into the frequency domain via the discrete cosine transform, performs flow matching in coefficient space, and reconstructs continuous trajectories using cosine basis expansion. A first-order temporal derivative regularization is introduced to enhance temporal consistency and smoothness. Without additional network parameters, FAFM significantly improves success rates, multimodal expressiveness, convergence speed, and robustness to mixed-frequency inputs and mechanical discrepancies across synthetic benchmarks, obstacle avoidance, LapGym, and LIBERO tasks, with real-world deployment validated on a Franka robot.

Abstract

Flow matching has emerged as a standard paradigm for robotic manipulation owing to its strong expressive power for modelling complex, multimodal action distributions, alongside similar approaches like diffusion policy. However, existing methods rely on discretized action chunks, making them brittle to demonstrations collected at heterogeneous control frequencies and prone to temporally inconsistent actions that degrade control stability. In this paper, we propose Frequency-Aware Flow Matching (FAFM), which outputs continuous, temporally consistent actions. To handle heterogeneous frequency input, we transform discrete action sequences into the frequency domain with the discrete cosine transform (DCT), perform flow matching over the resulting coefficients, and reconstruct continuous actions via cosine basis expansion. To generate temporally consistent actions, we regularize the first-order temporal derivative to promote smooth actions. This corresponds to a Sobolev-type constraint that suppresses high-frequency errors and discourages abrupt action changes. Our FAFM is simple, introduces no additional network parameters and applies to standalone flow-matching policies and vision-language action models. Across synthetic toy benchmark, obstacle avoidance, LapGym, and LIBERO, FAFM improves success rates, multimodal expressivity, motion smoothness, convergence speed, robustness to mechanical bias and mixed-frequency input. These gains are consistent when deployed on a real-world Franka robot. Code available at https://anonymous.4open.science/r/FAFM.

Problem

• flow matching
• action generation
• temporal consistency
• control frequency
• robotic manipulation

Innovation

• Flow Matching
• Frequency Domain
• Temporal Consistency
• Discrete Cosine Transform
• Sobolev Regularization