Offset-free model predictive control of a soft manipulator using the Koopman operator

The modeling and control of soft manipulators remain challenging due to their inherent complex kinematics and dynamics. This paper presents an offset-free Koopman operator-based model predictive control (OK-MPC) scheme that offers a practical data-driven approach to model and control the soft manipulator in the task space. In this scheme, the Koopman operator is used to derive a straightforward linear model to describe the complex dynamics of a soft manipulator. Then, an offset-free control strategy is incorporated with the Koopman operator to minimize the effect of modeling uncertainties and external disturbance, allowing the precise control of the soft manipulator. The proposed OK-MPC scheme was examined on both a soft pneumatic manipulator and a cable -driven origami manipulator through trajectory tracking experiments. The experimental results showed that the tracking errors decreased by 30.0% in free space and 45.4% in confined space, indicating that the OK-MPC has the capability to improve the control performance of a normal Koopman-based controller. Besides, the OK-MPC is readily available for the two different soft robotic prototypes, demonstrating its general applicability for the modeling and control in the field of soft robotics.