Continuum robots exhibit high-dimensional, nonlinear dynamics which are often coupled with their actuation mechanism. Spectral submanifold (SSM) reduction has emerged as a leading method for reducing high-dimensional nonlinear dynamical systems to low-dimensional invariant manifolds. Our proposed control-augmented SSMs (caSSMs) extend this methodology by explicitly incorporating control inputs into the state representation, enabling these models to capture nonlinear state-input couplings. Training these models relies solely on controlled decay trajectories of the actuator-augmented state, thereby removing the additional actuation-calibration step commonly needed by prior SSM-for-control methods. We learn a compact caSSM model for a tendon-driven trunk robot, enabling real-time control and reducing open-loop prediction error by 40% compared to existing methods. In closed-loop experiments with model predictive control (MPC), caSSM reduces tracking error by 52%, demonstrating improved performance against Koopman and SSM based MPC and practical deployability on hardware continuum robots.

翻译：连续体机器人展现出高维、非线性的动力学特性，且这些特性常与其驱动机制相互耦合。谱子流形（SSM）约简已成为将高维非线性动力系统降至低维不变流形的主流方法。我们提出的控制增强型SSM（caSSM）通过将控制输入显式纳入状态表征来扩展该方法论，使模型能够捕捉非线性状态-输入耦合关系。此类模型的训练仅依赖于致动器增强状态的受控衰减轨迹，从而消除了先前SSM控制方法所需额外驱动校准步骤。针对腱驱动躯干机器人，我们学习了紧凑的caSSM模型，实现了实时控制能力，并将开环预测误差较现有方法降低40%。在采用模型预测控制（MPC）的闭环实验中，caSSM将跟踪误差降低52%，展现出相较基于Koopman算子及SSM的MPC方法的性能提升，并具备在硬件连续体机器人上的实际部署可行性。