Data-Driven Dynamics Modeling of a 9-Degree-of-Freedom Rehabilitation Robot Based on the Koopman Operator

A study has been conducted on the dynamics of a serial-parallel hybrid redundant actuation rehabilitation robot. Compared to traditional robots, the dynamic modeling of redundant robots presents greater challenges. The number of actuators exceeds the minimum degrees of freedom (DOFs) required to complete the task, leading to multiple solutions for task planning. As the number of DOFs increases, so does the number of state variables in the dynamic equations, with the coupling effects between joints resulting in a highly nonlinear relationship among joint forces, velocities, and accelerations. Consequently, deriving a dynamic mechanistic model based on Lagrange or Newton-Euler equations becomes increasingly complex. In recent years, Koopman operator theory has attracted growing attention in the modeling of nonlinear dynamic systems. The core idea behind this theory is to lift nonlinear systems into a high-dimensional space, where their evolution can be described by linear operators. Extended Dynamic Mode Decomposition (EDMD) is a tool that facilitates the implementation of linear dimensionality expansion and the modeling of system dynamics. This study adopts the EDMD-based Koopman operator method to establish the dynamic model of the redundant robot, transforming nonlinear problems into linear ones in high-dimensional space. This approach circumvents the complex derivation and solution of nonlinear equations, thereby simplifying model construction. The resulting dynamic model demonstrates high predictive accuracy.