BKMPC-ESO: A data-driven bilinear model predictive control framework for soft robots with unknown nonlinear dynamics compensation

Abstract

In this paper, we introduce a novel control framework, termed BKMPC-ESO, which integrates bilinear Koopman model predictive control (BKMPC) with an extended state observer (ESO) for the modeling and control of soft robots. This framework specifically addresses the challenges posed by modeling errors and unknown disturbances, which often degrade the control performance of soft robots. It leverages the data-driven bilinear Koopman model to merge the computational efficiency of linear models with the predictive precision of nonlinear models, thereby adapting to the dynamics of diverse systems. Furthermore, the ESO is incorporated for real-time estimation of modeling errors and external disturbances, with these estimates being dynamically compensated within the MPC. This approach effectively mitigates the limitations of the offline bilinear Koopman model in capturing real-time parameter variations and external disturbances, enhancing the system’s control precision. Notably, the proposed BKMPC approach guarantees recursive feasibility and stability across an extended prediction horizon, with the stability of the ESO being rigorously validated through theoretical analysis. The efficacy of our framework is exemplified through its application on a three-dimensional (3D) soft manipulator. It is able to adeptly track a variety of reference trajectories, ranging from simple to complex, thereby highlighting the framework’s potential to significantly enhance the performance capabilities of soft robotic systems.