Learning a Resolution-Consistent Jacobian Field for Bio-Inspired Rigid-Soft Finger
This preprint introduces Jacobian Flow Matching (JFM), a Conditional Flow Matching-based learned Jacobian field for a tendon-driven rigid-soft finger. On real finger data, it cuts global average single-step RMSE by over 53% versus a pointwise baseline and improves sparse-sampling trajectory fidelity, reducing median RMSE by 14.43% at stride 8. It matters because it gives compliant dexterous hands a resolution-consistent local model usable for both prediction and trajectory optimization.
Can a resolution-consistent learned Jacobian field, trained with flow matching and intra-step supervision, improve finite-step motion prediction and rollout consistency for a tendon-driven rigid-soft finger across different sampling resolutions?
Tendon-driven rigid-soft fingers have configuration-dependent sensitivity, hysteresis, friction, and compliant nonlinearities, so analytical Jacobians are hard to maintain. Pointwise learned Jacobians degrade when the control or sensing step size changes, and they behave poorly under ODE integration because they lack constraints on intermediate states.
Model-based methods such as piecewise constant curvature, Cosserat rods, and finite-element models require simplifying assumptions and repeated identification under wear or routing changes. Learning-based methods often learn a pointwise Jacobian or end-to-end policy; these are tied to fixed step sizes and do not enforce consistency along continuous trajectories, making them brittle under sparse sampling or ODE rollout.
JFM models the actuation-to-motion relation as a continuous-time Jacobian field conditioned on the initial state, actuator command, and normalized time. It uses a TinyTransformer or LSTM backbone, Conditional Flow Matching-style bridge-path sampling for dense within-step supervision, and a dual-view consistency loss to reduce start-pose bias. The same trained network supports both single-step pointwise queries and multi-step ODE integration.
On a real middle finger with in-plane flexion, JFM reduced global average RMSE by 57.27% with a TinyTransformer backbone and 53.68% with an LSTM backbone compared with a pointwise baseline. Averaged across DIP, PIP, and MCP joints, 96.2% of JFM errors fell below 0.015 RMSE versus 77.9% for the baseline. Under sparse sampling at stride 8, ODE-based rollout improved RMSE median by 14.43% and reduced variance by 24.87% compared with pointwise inference. Inverse open-loop planning achieved an overall RMSE of 1.4151, mean error of -0.2576 degrees, and standard deviation of 1.39. Pointwise inference ran at approximately 3.5 ms per query. Evaluation used 160 test trajectories.
Authors state that the work covers only a single middle finger with in-plane flexion/extension, offline open-loop validation, and no closed-loop real-time control. Hard stops are predicted smoothly rather than instantaneously because boundary conditions are not modeled. Multi-finger coordination, out-of-plane motion, and real-time ODE-based control are left for future work. Evident limitations include a single hardware platform, unreported full training-set size, no code release stated, and limited task diversity.
Soft robotic hand and gripper manufacturers, prosthetics developers, and dexterous manipulation researchers could use JFM-style local models for trajectory optimization and model-based control. Near-term use within 1–3 years is plausible for offline planning and single-finger/single-plane tasks. Broader multi-finger closed-loop products likely require 3+ years, conditional on real-time ODE acceleration, multi-finger validation, and larger datasets.
The full text is not republished here because the paper's license does not allow it. Read the original on arXiv.