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<p>Soft robots offer a wide array of advantages in many fields thanks to their excellent compliance and environmental adaptability. However, their inherent flexibility and pronounced nonlinear characteristics present challenges for modeling and control. Currently, researchers have proposed a data-driven model predictive control (MPC) approach based on the Koopman operator, known as KMPC framework, which aims to address the challenges in soft robot modeling and control. This control framework has been experimentally verified on soft robots, demonstrating its effectiveness in practice. However, the performance of the framework is highly reliant on the data-driven Koopman modeling accuracy. Unlike the existing scheme mainly emphasizing the precision improvement of the Koopman model, a modified control strategy within the original KMPC framework is developed to further enhance the control effectiveness and adaptability in soft robotic systems. Specifically, this paper integrates the variable-structure reduced-order extended state observer (RESO) and Kalman filter (KF) into KMPC framework, referred to as KMPC-RESO-KF framework. It is noted that the RESO can mitigate the initial peak phenomenon, while the KF acts as a pre-filter to handle measurement noise and prepare the necessary signals for the RESO. The RESO-KF allows for real-time estimation of unmodeled dynamics from the Koopman model and external disturbances, thus balancing the speed and accuracy of state reconstruction, as well as the sensitivity to measurement noise. Subsequently, the unmodeled dynamics and external disturbances are handled as a total disturbance, which can be alleviated in a modified MPC algorithm using the saturation-like function on the lifted linear system with constraints. Significantly, the proposed MPC is proven to guarantee recursive feasibility and stability throughout a sufficiently long prediction horizon, and the stability of RESO-KF is theoretically verified as well. Eventually, the superiority of the proposed KMPC-RESO-KF framework is demonstrated through simulations and experiments in terms of the overall tracking control performance.</p>

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Data-driven predictive tracking control of soft robots: a Koopman-MPC framework integrated with variable structure reduced-order extended state observer and Kalman filter

  • 期刊论文

  • 发表日期：

    2025年5月9日

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  • Yunbei Li,
  • Zhaobing Liu

摘要

Soft robots offer a wide array of advantages in many fields thanks to their excellent compliance and environmental adaptability. However, their inherent flexibility and pronounced nonlinear characteristics present challenges for modeling and control. Currently, researchers have proposed a data-driven model predictive control (MPC) approach based on the Koopman operator, known as KMPC framework, which aims to address the challenges in soft robot modeling and control. This control framework has been experimentally verified on soft robots, demonstrating its effectiveness in practice. However, the performance of the framework is highly reliant on the data-driven Koopman modeling accuracy. Unlike the existing scheme mainly emphasizing the precision improvement of the Koopman model, a modified control strategy within the original KMPC framework is developed to further enhance the control effectiveness and adaptability in soft robotic systems. Specifically, this paper integrates the variable-structure reduced-order extended state observer (RESO) and Kalman filter (KF) into KMPC framework, referred to as KMPC-RESO-KF framework. It is noted that the RESO can mitigate the initial peak phenomenon, while the KF acts as a pre-filter to handle measurement noise and prepare the necessary signals for the RESO. The RESO-KF allows for real-time estimation of unmodeled dynamics from the Koopman model and external disturbances, thus balancing the speed and accuracy of state reconstruction, as well as the sensitivity to measurement noise. Subsequently, the unmodeled dynamics and external disturbances are handled as a total disturbance, which can be alleviated in a modified MPC algorithm using the saturation-like function on the lifted linear system with constraints. Significantly, the proposed MPC is proven to guarantee recursive feasibility and stability throughout a sufficiently long prediction horizon, and the stability of RESO-KF is theoretically verified as well. Eventually, the superiority of the proposed KMPC-RESO-KF framework is demonstrated through simulations and experiments in terms of the overall tracking control performance.