A Flow Matching Framework for Soft-Robot Inverse Dynamics

arXiv cs.RO / 4/6/2026

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Key Points

The paper tackles soft continuum robot inverse dynamics by learning differential dynamics for open-loop feedforward control, addressing high-dimensional nonlinearities and actuation coupling that make conventional control difficult.
It reformulates inverse dynamics as a conditional flow-matching problem and uses Rectified Flow to generate physically consistent control inputs rather than relying on regression to conditional averages.
Two variants improve physical consistency: RF-Physical adds a physics-based prior for residual modeling, while RF-FWD enforces forward-dynamics consistency via an additional loss during flow matching.
Experiments show more than 50% reduction in trajectory tracking RMSE versus standard deterministic regression baselines (MLP, LSTM, Transformer) and stable open-loop execution up to 1.14 m/s end-effector velocity.
The method reports sub-millisecond inference latency (~0.995 ms), indicating suitability for real-time control in soft-robot settings.

Abstract

Learning the inverse dynamics of soft continuum robots remains challenging due to high-dimensional nonlinearities and complex actuation coupling. Conventional feedback-based controllers often suffer from control chattering due to corrective oscillations, while deterministic regression-based learners struggle to capture the complex nonlinear mappings required for accurate dynamic tracking. Motivated by these limitations, we propose an inverse-dynamics framework for open-loop feedforward control that learns the system's differential dynamics as a generative transport map. Specifically, inverse dynamics is reformulated as a conditional flow-matching problem, and Rectified Flow (RF) is adopted as a lightweight instance to generate physically consistent control inputs rather than conditional averages. Two variants are introduced to further enhance physical consistency: RF-Physical, utilizing a physics-based prior for residual modeling; and RF-FWD, integrating a forward-dynamics consistency loss during flow matching. Extensive evaluations demonstrate that our framework reduces trajectory tracking RMSE by over 50% compared to standard regression baselines (MLP, LSTM, Transformer). The system sustains stable open-loop execution at a peak end-effector velocity of 1.14 m/s with sub-millisecond inference latency (0.995 ms). This work demonstrates flow matching as a robust, high-performance paradigm for learning differential inverse dynamics in soft robotic systems.