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.

Vehicular Applications of Koopman Operator Theory—A Survey

“…The operation of robotic arms was found to be the most common application in this category and has been treated as a "vehicle" for the purposes of this survey as such devices are usually employed to spatially transport a payload from one point to another. For this purpose, EDMD was used (which they refer to as Koopman-MPC) to actuate the arm under voltage disturbance [34]. An aforementioned study from the Aerospace category [58] also demonstrates DMDc and other approaches including ANN and Reinforcement Learning on a robotic arm.…”

Data-Driven Model Predictive Control for Uncalibrated Visual Servoing

“…Koopman operator theory provides a data-driven solution by constructing a linear model of the nonlinear dynamical system, enabling the use of linear control methods like linear quadratic regulators (LQRs) and linear MPC [33]. For instance, Zhu et al [34] proposed a Koopman MPC (KMPC) approach for trajectory tracking control of an omnidirectional mobile manipulator. Bruder et al [35] designed MPC controllers for a pneumatic soft robot arm via the Koopman operator and demonstrated that the KMPC controllers outperform the MPC controller based on the linearized model, making accurate linear control of nonlinear systems achievable.…”

“…We choose observable functions to contain the original state x(k) as (34); then, the linear Koopman model ( 29) could be constructed, where…”