Koopman Operator-Based Data-Driven Online Learning Control for an Omni-Directional Mobile Manipulator

Omni-directional mobile manipulators (OMMs) are typically nonlinear, strongly coupled, multiple-input and multiple-output systems, for which the development of mechanistic models is often complex and time-consuming. Koopman operator theory is a fully data-driven modeling approach that leverages input-output data to generate high-dimensional linear models, but it often has modeling errors. In this paper, a completely data-driven online learning linear model predictive control (MPC) framework is proposed for an OMM, without using any prior knowledge of the robot system. A finite-dimensional approximate linear Koopman model is established for an OMM using the input-output data. The model errors (including external disturbances) are online learned by Gaussian process regression (GPR) using the collected data and compensated for in real time within the controller. Selective forgetting and incremental inverse computation methods are employed to reduce the computational cost of online GPR. Finally, a total of 11,400 experimental data pairs are generated for Koopman modeling of an OMM prototype, utilizing randomly generated control inputs under different initial states. Then experimental tests are carried out to verify the control performances and robustness of the proposed control scheme.