On the learning-based control of continuum robots with provable robustness, efficiency, and generalizability

Recent years have witnessed the remarkable advancements in Koopman-operator-based data-driven methods for continuum robot control. However, there is currently a paucity of both theoretical and practical work investigating the convergence and robustness of these methods, which is crucial due to the complexity and susceptibility of continuum robots and the training-to-reality gap. This work seeks to complete Koopman-operator-based methods in terms of accuracy, robustness, generalizability, and theoretical analysis while maintaining high computational efficiency. In this work, we learn the continuous-time model of continuum robots using a deep Koopman network, which bridges the gap between unknown robot models and model-dependent iterative learning control, and propose a novel control framework for data-driven control of continuum robots. Rigorous theoretical analysis is then provided to prove the convergence and robustness of the proposed method. Finally, comprehensive comparisons of three types of Koopman-operator-based methods are conducted, using six metrics to evaluate their performance. Experiments on two heterogeneous continuum robots indicate that our proposed method outperforms existing Koopman-operator-based control methods across most metrics, significantly improving robustness and generalizability. Furthermore, this work has guiding significance for applying Koopman-operator-based control methods to the efficient and robust control of other robotic systems.