Organizations: College of Intelligence Science and Technology, National University of Defense Technology,, Changsha, 410073, China · National Key Laboratory of Equipment State Sensing and Smart Support, National University of Defense Technology,, Changsha, 410073, China
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.
Tendon-Driven Continuum Robots (TDCRs) pose significant control challenges due to their highly nonlinear, path-dependent dynamics and non-Markovian characteristics. Traditional Jacobian-based controllers often struggle with hysteresis-induced oscillations, while conventional learning-based approaches suffer from poor generalization to out-of-distribution trajectories. This paper proposes a reference-augmented offline learning framework for precise 6-DOF tracking control of TDCRs. By leveraging a differentiable RNN-based dynamics surrogate as a gradient bridge, we optimize a control policy through an augmented reference distribution. This multi-scale augmentation scheme incorporates stochastic bias, harmonic perturbations, and random walks, forcing the policy to internalize diverse tracking error recovery mechanisms without additional hardware interaction. Experimental results on a three-section TDCR platform demonstrate that the proposed policy achieves a 50.9% reduction in average position error compared to non-augmented baselines and significantly outperforms Jacobian-based methods in both precision and stability across various speeds. For implementation details and source code, please refer to https://github.com/ZiqingZou/ContinuumControl.
Ziqing Zou, Ke Qiu, Haojian Lu +2
Department of Control Science and Engineering, Zhejiang University, Hangzhou, China
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.
Fabian Schwab, Federico Allione, Bingcheng Wang +5
1Engineering Sciences Department, Swiss Federal Laboratories for Materials Science and Technology, Switzerland · Institute for NeuroInformatics, University of Zurich, Switzerland · Department of Electronic Engineering, University of Rome Tor Vergata, Italy
Tendon-Driven Continuum Robots (TDCRs) pose significant modeling and control challenges due to complex nonlinearities, such as frictional hysteresis and transmission compliance. This paper proposes a differentiable learning framework that integrates high-fidelity dynamics modeling with robust neural control. We develop a GRU-based dynamics model featuring bidirectional multi-channel connectivity and residual prediction to effectively suppress compounding errors during long-horizon auto-regressive prediction. By treating this model as a gradient bridge, an end-to-end neural control policy is optimized through backpropagation, allowing it to implicitly internalize compensation for intricate nonlinearities. Experimental validation on a physical three-section TDCR demonstrates that our framework achieves accurate tracking and superior robustness against unseen payloads, outperforming Jacobian-based methods by eliminating self-excited oscillations. For implementation details and source code, please refer to https://github.com/ZiqingZou/ContinuumControl.
Ziqing Zou, Ke Qiu, Fei Wang +3
Department of Control Science and Engineering, Zhejiang University, Hangzhou, China