Learning-Based Dynamics Modeling and Robust Control for Tendon-Driven Continuum Robots

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.

Developing dynamic models for tendon-driven continuum robots is challenging due to their nonlinear, high-dimensional, and friction-dominated dynamics. This paper presents a comparative study of data-driven system identification methods, including N4SID, ARX, and SINDYc, for modeling a tendon-actuated continuum robot with rolling joints developed at CERN. Despite the high number of joints of the robot, experimental analysis reveals that a two-degree-of-freedom dynamic model can accurately capture the system dynamics, owing to strong kinematic dependencies between the joints. The models are validated against experimental data, and used in the design of a model predictive controller, demonstrating their feasibility for real-time control.

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.