Koopman-Operator-Based Robust Data-Driven Control for Wheeled Mobile Robots

The Koopman operator theory offers a way to construct explicit control-oriented high-dimensional linear dynamical models for the original nonlinear systems, solely using the input-output data of the dynamical system. The modeling accuracy of the Koopman model largely depends on the basis functions (lifting functions), dimensionality, and data quality. However, there has not been a systematic way to solve the problems mentioned above. In this article, a Koopman-operator-based robust data-driven control framework is proposed for wheeled mobile robots, via incorporating tools from control theory, to solve the problem of modeling errors of the Koopman model. By employing an extended state observer, the modeling errors of the Koopman model, including unknown external disturbances, are online estimated and compensated in the control signal in real time. Then, sliding-mode control is used to synthesize the controller. Importantly, the method of virtual control input is proposed, to cope with the model errors arising from the rotational motion of all the mobile robots. Besides, stability analysis is conducted, and the optimal dimensionality of the Koopman model is experimentally selected. Finally, experimental tests on an omnidirectional mobile robot are carried out to verify the effectiveness of the proposed control scheme, in terms of tracking performance and robustness.