Decoupled Time-Delay Koopman Learning for Adaptive Model Predictive Control of Soft Manipulators

Abstract

The modeling and control of soft pneumatic manipulators present significant challenges due to their inherent compliance and history-dependent hysteresis. While the Koopman operator theory offers a promising solution by embedding these nonlinear dynamics into a linear framework, conventional Koopman approaches are limited by static models that fail to adapt to time-varying environments. To address this limitation, this study proposes a decoupled time-delay Koopman learning framework integrated with adaptive model predictive control. Specifically, a neural network with time-delay embedding is constructed to explicitly capture memory effects inherent in soft materials. Crucially, by incorporating a variance-covariance regularization strategy, the method enforces feature orthogonality during the learning of time-delay dynamics. This decoupling significantly reduces linear redundancy, thereby improving the numerical conditioning of the recursive least-squares updates and enhancing the efficiency of the feature dimension. Extensive experiments demonstrate that the proposed method achieves improved trajectory tracking accuracy and robustness, especially in low-dimensional lifting spaces. A Diamond robot simulation in SOFA and a physical tube manipulation task were conducted to validate the effectiveness of the proposed controller.