# History-Conditioned Flow Matching for Probabilistic Dynamics of Tendon-Driven Continuum Robots

arXiv: https://arxiv.org/abs/2609.25658 · HTML: https://mlsanity.com/paper/2609.25658/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models.
- Builds on 13 of its 28 references that are in the map.
- First posted on arXiv 22 Sep 2026.

## Placed in

- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)

## Builds on (most cited first, 13 of 13)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Multimodal Deep Generative Models for Trajectory Prediction: A Conditional Variational Autoencoder Approach](https://mlsanity.com/paper/2008.03880/) (2020)
- [Soft Robots Modeling: a Structured Overview](https://mlsanity.com/paper/2112.03645/) (2021)
- [Fast and Robust Visuomotor Riemannian Flow Matching Policy](https://mlsanity.com/paper/2412.10855/) (2024)
- [Data-driven Methods Applied to Soft Robot Modeling and Control: A Review](https://mlsanity.com/paper/2305.12137/) (2023)
- [Efficient Trajectory Forecasting and Generation with Conditional Flow Matching](https://mlsanity.com/paper/2403.10809/) (2024)
- [SpiRobs: Logarithmic Spiral-shaped Robots for Versatile Grasping Across Scales](https://mlsanity.com/paper/2303.09861/) (2023)
- [Accounting for Hysteresis in the Forward Kinematics of Nonlinearly-Routed Tendon-Driven Continuum Robots via a Learned Deep Decoder Network](https://mlsanity.com/paper/2404.03816/) (2024)
- [Modeling Kinematic Uncertainty of Tendon-Driven Continuum Robots via Mixture Density Networks](https://mlsanity.com/paper/2404.04241/) (2024)
- [Model Predictive Control for a Soft Robotic Finger with Stochastic Behavior based on Fokker-Planck Equation](https://mlsanity.com/paper/2509.01065/) (2025)
- [A Stochastic Framework for Continuous-Time State Estimation of Continuum Robots](https://mlsanity.com/paper/2510.01381/) (2025)

## Abstract (arXiv)

Deterministic dynamics modeling of tendon-driven continuum robots remains challenging owing to uncertainties in material behavior, tendon transmission, friction, and contact. Measured joint configurations and nominal tendon commands do not fully characterize these internal mechanical factors, leaving uncertainty in the subsequent motion. We therefore develop a history-conditioned, physics-informed flow-matching framework for probabilistic dynamics prediction, using motion and actuation histories to predict the distribution of the next complete joint configuration. By recursively sampling next-step configurations under prescribed commands, the model predicts distributions of future whole-body motions. In simulation, scenario-specific models achieve five-second trajectory Energy Scores (lower is better) of 12.05 mm under internal friction variation and 9.29 mm under unobserved actuation disturbances. Relative to the conditional variational autoencoder and diffusion baselines, Flow attains lower Energy Scores and coverage closer to the nominal level in both scenarios. Ablations support history and structural conditioning in both scenarios. On the physical robot, predictions under two tendon-command profiles excluded from training capture the principal motion sequences, with five-second Energy Scores of 11.91 and 11.42 mm, lower than the compared baselines. The predicted-to-measured spread ratios are 1.65 and 1.22 (closer to 1 is better). These results support history-conditioned probabilistic dynamics prediction under incomplete mechanical observations.