Koopman operator based model predictive control for trajectory tracking of an omnidirectional mobile manipulator

Abstract

Omnidirectional mobile manipulators (OMMs) have been widely used due to their high mobility and operating flexibility. However, since OMMs are complex nonlinear systems with uncertainties, the dynamic modeling and control are always challenging problems. Koopman operator theory provides a data-driven modeling method to construct explicit linear dynamic models for the original nonlinear systems, using only input-output data. It then allows to design control system based on well-established model-based linear control methods. This paper designs a Koopman operator based model predictive control (MPC) scheme for trajectory tracking control of an OMM. Firstly, using Koopman operator and extended dynamic mode decomposition method, an approximate high-dimensional linear dynamic explicit expression for the OMM system is obtained. Then MPC is employed to achieve tracking control based on the derived linear Koopman model. Finally, to show modeling accuracy for the OMM, the Koopman model is evaluated via both simulation and experimental tests. The control performances of the Koopman operator based MPC design are also verified in the simulation and experimental results.