Koopman Explicit Model Following Control Framework for a Robotic Manipulator

Robotic manipulators have nonlinear and coupled dynamics, and this situation makes accurate modeling and control difficult under parameter uncertainties and external effects. Despite the numerous suggestions for adaptive, learning-based and robust controllers, their effectiveness often depends on accurate dynamic models. The Koopman operator framework offers a data-driven alternative by representing nonlinear dynamics through linear evolution in a lifted observable space, with extended-state formulations capturing states, control inputs, and physics-informed features for improved fidelity. This paper proposes a Koopman Explicit Model Following Control (KEMFC) framework that integrates extended-state Koopman identification with Explicit Model Following Control (EMFC) for robot manipulators exhibiting nonlinear dynamics. An extended-state Koopman identification is accomplished to predict control torque from the positions and velocities of the robot manipulators. The identified Koopman operator is integrated with an EMFC law to enhance tracking performance under the presence of load, friction, and uncertainties. Numerical simulations of a three-degree-of-freedom anthropoid robotic manipulator demonstrate enhanced tracking precision and robustness. The simulation results demonstrate that KEMFC provides a systematic, data-driven methodology for model-following control for robotic systems, outperforming traditional model-based computed torque control.