A Flow Matching Framework for Soft-Robot Inverse Dynamics

Hang Yang; Fangju Yang; Yangming Zhang; Ibrahim Alsarraj; Yuhao Wang; Zhenye Luo; Zixi Chen; Ke Wu

cs.ROApr 3, 2026

A Flow Matching Framework for Soft-Robot Inverse Dynamics

Authors: Hang Yang, Fangju Yang, Yangming Zhang, Ibrahim Alsarraj, Yuhao Wang, Zhenye Luo, Zixi Chen, Ke Wu

Abstract

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.

Figures & tables

Fig. 1 : Flow-matching-based open-loop feedforward controller. The framework solves the inverse-dynamics problem by iteratively mapping desired state transitions to control inputs through learned flow matching.

Panel of Figure 2 — Fig. 2 : Trajectory ( $y-z$ ) comparison. Top: Inverse MLP/LSTM/Transformer. Bottom: RF/RF-Phys/RF-FWD.

Panel of Figure 3 — Fig. 3 : Input comparison ( $u_{1}/u_{2}$ ). Top: Inverse MLP/LSTM/Transformer. Bottom: RF/RF-Phys/RF-FWD.

Model	Shape Traj. RMSE	Random Traj. RMSE
MLP	23.1	30.6
LSTM	15.6	8.4
Transformer	13.4	12.7
RF	6.7	5.2
RF-FWD	5.0	3.5
RF-Physical	6.8	4.0

TABLE I : Open-loop trajectory-tracking RMSE (mm).

Model	Phase Lag (Shape)	Input Energy (Rand)
MLP	0.0575 s	26.47
LSTM	0.0775 s	16.56
Transformer	0.0475 s	20.70
RF-FWD	0.0450 s	17.04

TABLE II : Phase lag and input energy of the generated control signals.

Fig. 4 : The circular reference trajectories with high speed in simulation.

Panel of Figure 7 — Fig. 5 : Complex trajectory comparison and input results.

Fig. 7 : High-speed circular reference tracking in experiments.

Panel of Figure 10 — Fig. 8 : Vertical plane trajectory tracking performance. (a)-(d) 2D plots of the end-effector position against reference paths. The transient trajectory from the Initial point ( $\diamond$ ) to the Start point ( $\bullet$ ) is excluded from the tracking performance evaluation. (e)-(h) Stroboscopic composite images showing the tracking ball’s motion at 0.4 s intervals. Visualization note: Backgrounds in the bottom row were darkened and color-enhanced for contrast.

Panel of Figure 11 — Fig. 9 : Horizontal plane trajectory tracking performance.

Trajectory	Vertical RMSE (mm)	Horizontal RMSE (mm)
Star	3.83	3.96
Spiral	4.94	6.52
Circle	3.95	8.65
Heart	4.46	6.47
Mean	4.30	6.40

TABLE III : Physical tracking RMSE under two gravity configurations (RF-FWD).

Method	Ctrl. Type	Infer. [ms]	Speed [m/s] ( $v/L$ [s -1 ])	Err. [mm (%L)]	Train [min]
OL-LSTM [ 30 ]	Feedforward	–	0.035–0.045 (0.18–0.23)	$\sim$ 3.2 (1.6%)	–
Dyn. Oper. [ 5 ]	Feedback	–	1.50 (3.23)	–	$<5$
DKoopman [ 17 ]	Feedback	0.44 $\pm$ 0.14	–	1.79 $\pm$ 1.26 (3.25%)	–
Hyb. MLNN [ 31 ]	Feedback	$<3.0$	0.005–0.080 (0.03–0.46)	0.4–1.1 (0.23–0.63%)	–
PINN-MPC [ 6 ]	Feedback	–	–	$<3.0$ (2.3%)	$>11520$
RF-FWD (Ours)	Feedforward	0.995	1.14 (2.53)	4.3–6.4 (0.96–1.42%)	20

TABLE IV : Comparison with representative soft-robot control frameworks.

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

Xingyu Chen, Yi Xiong, Li Wen

School of Mechanical Engineering and Automation, Beihang University, Beijing 100191, China

Cycle Consistency Robot Learning Soft Robotics Continuum Robot Control Long Short-Term Memory Networks

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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.

Abstract

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