Consistency-Driven Dual LSTM Models for Kinematic Control of a Wearable Soft Robotic Arm

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.

Soft robots have attracted much attention for their safe human-robot interaction and flexibility, but the typical continuum structure and nonlinear material behavior make the kinematics modelling complex, especially in non-static motions. In this work, we proposed an LSTM-based pressure predictive control (PPC) for the motion control of a vertebraic soft robotic tail and the coordination with a quadruped robot. The PPC consists of an inverse kinematics (IK) model, a forward kinematics (FK) model and a pressure compensation (P-comp) model, and achieves non-static and quasi-static motion control of the tail. Compared with the IK-only model, the average RMSE of the PPC's simulation trajectories reduces by 69.8%, when executing target trajectories. In the coordinated motions of the soft tail quadruped, using a prediction data set to train the PPC enables next-moment action prediction and reduces computation time by 60.9%, which enhances the real-time response of the tail to match the quadruped torso's moving rate. The PPC provides a simple and effective method to model the soft tail for both non-static and quasi-static motion control, and grants the soft tail quadruped with the functionality of interacting with the environment.

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.