Neural Network Augmented Koopman Explicit Model Following Control for Robotic Manipulators

This paper introduces a Neural Network Augmented Koopman Explicit Model Following Control (NNKEMFC) framework designed for robust trajectory tracking of robotic manipulators that exhibit nonlinear and uncertain dynamics. The proposed method integrates an offline-identified extended-state Koopman operator within an Explicit Model Following Control (EMFC) framework to produce a data-driven feedforward control action while maintaining a model-following structure. To tackle modeling errors, friction effects, external disturbances, and parametric uncertainties, an online neural network control structure is integrated to estimate unmodeled dynamics in real time. The final control input includes the Koopman-based feedforward torque, a filtered tracking-error feedback term, neural network compensation, and a robustifying signal to enhance robustness. The proposed approach is evaluated using a multi-degree-of-freedom robotic manipulator in several scenarios that include friction, external loads, and parameter uncertainties. Simulation results indicate that the NNKEMFC outperforms the classical computed torque control and KEMFC and achieves notable reductions in joint-space RMS tracking errors, particularly in nonlinear conditions. These results highlight the advantages of incorporating a Koopman-based model followed by online neural residual learning to enhance the robust tracking of robotic manipulators.