Robust Adaptive Koopman MPC Under Structured and Stochastic Uncertainty for Soft Continuum Robots

Soft continuum robots exhibit highly nonlinear and configuration-dependent dynamics, making accurate trajectory tracking challenging under model uncertainty and external disturbances. This paper presents an adaptive Koopman-based model predictive control (MPC) framework for a tendon-driven soft continuum robot and evaluates its performance through comprehensive closed-loop simulations. A lifted linear Koopman model is identified from experimentally collected robot data and incorporated into an MPC formulation to provide computationally efficient prediction while capturing dominant nonlinear behavior. To compensate for plant–model mismatch and time-varying uncertainties, an online Recursive Least Squares (RLS) adaptation mechanism is integrated into the Koopman–MPC framework, enabling continuous model refinement during closed-loop operation without repeated offline retraining. The proposed controller is evaluated through comprehensive closed-loop simulations on circular, triangular, helical, and figure-eight trajectories under stochastic disturbances and structured parametric bias conditions using a Koopman model identified from experimentally collected robot data. Results demonstrate consistent improvements in tracking performance compared with fixed Koopman MPC while maintaining real-time computational feasibility. Under structured parametric bias, the proposed controller reduces the mean tracking error from 9.30 mm to 1.36 mm during circular trajectory tracking and achieves sub-millimeter accuracy in several operating conditions. These findings highlight the potential of online Koopman model adaptation for predictive control of soft continuum robots operating under uncertainty.