A Flow Matching Framework for Soft-Robot Inverse Dynamics

In this paper, we introduce a consistency-driven dual LSTM framework for accurately learning both the forward and inverse kinematics of a pneumatically actuated soft robotic arm integrated into a wearable device. This approach effectively captures the nonlinear and hysteretic behaviors of soft pneumatic actuators while addressing the one-to-many mapping challenge between actuation inputs and end-effector positions. By incorporating a cycle consistency loss, we enhance physical realism and improve the stability of inverse predictions. Extensive experiments-including trajectory tracking, ablation studies, and wearable demonstrations-confirm the effectiveness of our method. Results indicate that the inclusion of the consistency loss significantly boosts prediction accuracy and promotes physical consistency over conventional approaches. Moreover, the wearable soft robotic arm demonstrates strong human-robot collaboration capabilities and adaptability in everyday tasks such as object handover, obstacle-aware pick-and-place, and drawer operation. This work underscores the promising potential of learning-based kinematic models for human-centric, wearable robotic systems.

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.

Soft robots are valuable robophysical platforms for studying body-caudal undulatory locomotion, but their compliant bodies are difficult to control precisely under changing hydrodynamic loading. Conventional proportional-integral-derivative (PID) feedback stabilizes periodic undulation in static water, but can accumulate flow-dependent tracking delay and increasing inter-trial variability when environmental flow becomes non-trivial. Here, we evaluate whether augmenting PID control with a Linear Repetitive Learning Estimation Scheme (PID-LRLES) recovers tracking accuracy and repeatability under dynamic flow. The LRLES generalizes classical integral action from constant to periodic, non-constant references, while using a stable transfer-function realization whose poles have negative real parts to avoid the long-term instability issues of classical repetitive control. Closed-loop experiments were carried out in a recirculating flow tank at five bulk flow speeds spanning 0 to 32.6 cm s^-1, using an embedded soft capacitive bending sensor at a 1 kHz control-loop rate. With controller gains tuned once in static water and then held fixed across all conditions, PID-LRLES tracked the periodic bending-envelope reference more closely than the PID baseline and significantly reduced the inter-trial spread of the per-trial RMSE (paired Wilcoxon signed-rank test, p = 1.8 x 10^-4, n = 25). Embedded soft proprioception and cycle-to-cycle learning act as complementary contributors to robustness: the sensor exposes the periodic hydrodynamic bias in body deformation, while the learning term absorbs it over recent oscillation cycles. By reducing flow-dependent control-induced variability, the approach provides an enabling layer for future robophysical studies seeking to isolate the effects of morphology, sensing, and environmental flow on aquatic locomotion.