Koopman Operator Modeling of the Cable-Driven Parallel Robots Based on the Deep-EDMD

The inherent flexibility and unilateral force characteristics of the cables impart complex nonlinear characteristics to the fully constrained cable-driven parallel robots (CDPRs), presenting significant challenges for the precise control of the system. To address this issue, a time-varying flexible multibody system dynamics model is established, incorporating the flexibility of the cables to accurately compute the dynamic characteristics of the system and acquire the input-output data of the controlled system. Subsequently, leveraging the extended dynamic mode decomposition algorithm, a Deep Extended Dynamic Mode Decomposition (Deep-EDMD) algorithm is proposed, which integrates deep learning techniques to approximate the selection of eigenfunctions of the Koopman operator for solving its finite-dimensional approximation. This approach enables the representation of the nonlinear dynamics model of the CDPR as a finite-dimensional linear dynamics model using the Koopman operator, thereby enhancing the model’s generalizability and accuracy, achieving global linearization, and facilitating subsequent controller design. Simulation results demonstrate that the finite-dimensional Koopman operator linear dynamics model based on the Deep-EDMD algorithm can accurately describe the dynamic characteristics of the original nonlinear system within a certain time frame.