Data-Driven Dynamic Modeling of a Tendon-Actuated Continuum Robot

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.

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.

Predicting the shape of tendon driven continuum robots (TDCRs) at steady state from actuation remains challenging due to continuous deformation, complex tendon routing, compliance, friction, and fabrication variability. In this paper, we address this problem as kinematic self modeling conditioned on action. We present a lightweight 3D printed TDCR hardware platform and an RGB-D data collection pipeline with multiple cameras, and we learn a point cloud flow matching model that maps motor actuation states to the robot's settled 3D geometry. The model is trained from randomly sampled quasi static configurations and evaluated on test motor commands within the same TDCR design family and actuation range. We compare against prior 3D deformable object and robot self modeling approaches in both MuJoCo simulation and real hardware experiments. Experiments on simulated 2-, 3-, and 5-module TDCRs and real 2- and 3-module robots show improved shape prediction accuracy under CD and EMD metrics. We further show in simulation that the same conditional formulation generalizes to tip payload as a conditioning input, enabling payload conditioned steady-state shape prediction. These results demonstrate a data driven self modeling framework for quasi static TDCR geometry prediction.