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A Flow Matching Framework for Soft-Robot Inverse Dynamics

Hang Yang, Fangju Yang, Yangming Zhang, Ibrahim Alsarraj, Yuhao Wang, Zhenye Luo, Zixi Chen, Ke Wu

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.

A Flow Matching Framework for Soft-Robot Inverse Dynamics

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.

Paper Structure

This paper contains 22 sections, 22 equations, 9 figures, 4 tables.

Table of Contents

  1. Introduction
  2. PROBLEM STATEMENT
  3. Task Objective and Robot Platform
  4. Main Challenges
  5. METHODOLOGY
  6. Problem Formulation: From Differential Dynamics to Iterative Inverse Mapping
  7. Rectified-Flow-Based Inverse-Dynamics Framework
  8. Training Loss
  9. Feedforward Control Inference
  10. EVALUATION IN SIMULATION
  11. System Setup and Data Acquisition
  12. Baseline Comparison
  13. Tracking Accuracy and Computational Cost
  14. Input Quality
  15. Robustness and Generalization Stress Test
  16. ...and 7 more sections

Figures (9)

  • Figure 1: Flow-matching-based open-loop feedforward controller. The framework solves the inverse-dynamics problem by iteratively mapping desired state transitions to control inputs through learned flow matching.
  • Figure 2: Trajectory ($y-z$) comparison. Top: Inverse MLP/LSTM/Transformer. Bottom: RF/RF-Phys/RF-FWD.
  • Figure 3: Input comparison ($u_1/u_2$). Top: Inverse MLP/LSTM/Transformer. Bottom: RF/RF-Phys/RF-FWD.
  • Figure 4: The circular reference trajectories with high speed in simulation.
  • Figure 5: 3D tip trajectory comparison (Reference vs RF-FWD).
  • ...and 4 more figures