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This research introduces Jacobian Flow Matching, a novel machine learning framework designed to model the complex nonlinear dynamics of bio-inspired rigid-soft robotic fingers. By treating actuation-to-motion transitions as a dynamical flow, the method achieves superior prediction accuracy and robustness against sparse sensor sampling compared to traditional discrete linear approximations. The approach advances the field of robot control by enabling high-fidelity trajectory optimization for highly coupled mechanical systems through structured learning techniques.
Learning a Resolution-Consistent Jacobian Field for Bio-Inspired Rigid-Soft Finger
arXiv:2610.01668v1 Announce Type: new Abstract: Bio-inspired tendon-driven rigid-soft coupled dexterous fingers exhibit strong nonlinearity and configuration-dependent sensitivity, making accurate modeling challenging. In discrete-time control, Jacobian-based kinematic algorithms typically rely on point-wise local linear approximations, which makes their performance sensitive to sensor sampling frequency and controller update frequency. To address this issue, we propose Jacobian Flow Matching (JFM), a structured learning framework based on Conditional Flow Matching (CFM), to learn a resolution-consistent Jacobian field that models actuation-to-motion transitions as a dynamical flow. The proposed framework supports both single-step prediction and continuous rollout via ODE integration, enabling consistent inference across temporal resolutions. Experiments on a tendon-driven rigid-soft finger show that the proposed method suppresses outlier errors and improves single-step prediction accuracy, reducing the global average RMSE by over 53% compared with a baseline discrete Jacobian learning approach. For long-horizon prediction, trajectories recovered via ODE integration achieve higher fidelity under sparse sampling (Stride = 8), reducing the RMSE median by 14.43% and the error variance by 24.87%. These results demonstrate that the learned flow-based Jacobian field provides an effective local model for offline multi-step trajectory optimization in rigid-soft coupled nonlinear systems.
Abstract:Bio-inspired tendon-driven rigid-soft coupled dexterous fingers exhibit strong nonlinearity and configuration-dependent sensitivity, making accurate modeling challenging. In discrete-time control, Jacobian-based kinematic algorithms typically rely on point-wise local linear approximations, which makes their performance sensitive to sensor sampling frequency and controller update frequency. To address this issue, we propose Jacobian Flow Matching (JFM), a structured learning framework based on Conditional Flow Matching (CFM), to learn a resolution-consistent Jacobian field that models actuation-to-motion transitions as a dynamical flow. The proposed framework supports both single-step prediction and continuous rollout via ODE integration, enabling consistent inference across temporal resolutions. Experiments on a tendon-driven rigid-soft finger show that the proposed method suppresses outlier errors and improves single-step prediction accuracy, reducing the global average RMSE by over 53% compared with a baseline discrete Jacobian learning approach. For long-horizon prediction, trajectories recovered via ODE integration achieve higher fidelity under sparse sampling (Stride = 8), reducing the RMSE median by 14.43% and the error variance by 24.87%. These results demonstrate that the learned flow-based Jacobian field provides an effective local model for offline multi-step trajectory optimization in rigid-soft coupled nonlinear systems.
27 pages, 8 figures, including supplementary material. Under review at Robotics and Autonomous Systems
Robotics (cs.RO)
arXiv:2610.01668 [cs.RO]
(or arXiv:2610.01668v1 [cs.RO] for this version)
https://doi.org/10.48550/arXiv.2610.01668 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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