Inspired by soft creatures and structures in nature, continuum robots exhibit remarkable flexibility, safe interaction, and ease of miniaturization, showcasing vast application potential. However, their flexible structure renders analytical methods inadequate for precise modeling and control, while existing data-driven approaches suffer from low data efficiency and unproven theoretical control performance. This paper aims to achieve data-efficient modeling and reliable control of continuum robots through innovative algorithms, exploring the performance of the new method from both theoretical and experimental perspectives. Specifically, we utilize neural ordinary differential equations (NODE) to achieve data-efficient modeling of continuum robots and investigate the performance of the modeling method. Then, we propose a novel predefined-time-synchronized stable zeroing neurodynamics (PTSS-ZND) model. By combining the NODE method and the PTSS-ZND method, we propose a reliable data-driven control system. Through rigorous theoretical analysis, we prove the stability and predefined-time convergence of the data-driven control system. Finally, through simulations and physical experiments, we validate the feasibility and convergence of the novel method and its advantages over existing data-driven methods. Experiments on one- and three-segment continuum robots indicate that the proposed method achieves a root mean square position error (e.g., 2.5 mm for the three-segment robot) of less than 1% of the robot length using fewer than 100 data samples. Our method also demonstrates robust performance under various external and internal disturbances. In addition, it can potentially be extended for end-effector pose control.

Traditional data-driven control methods often require large amounts of training data, posing significant challenges for continuum robots. Recently, neural ordinary differential equation (NODE) methods have demonstrated impressive capabilities for data-efficient modeling of continuum robots. However, existing NODE-based control methods still face limitations in terms of convergence and robustness. In this paper, we propose a data-driven iterative learning control system for continuum robots, leveraging NODE for modeling. Within this framework, by incorporating online parameter learning, the proposed control system continuously adapts to various uncertainties associated with continuum robots, resulting in improved convergence and robustness in repetitive tasks. The effectiveness of the proposed method is validated through simulations and physical experiments, and comparative analysis highlights its superior accuracy over existing approaches.