Robust Position Control of a Continuum Manipulator Based on Selective Approach and Koopman Operator

Robust Position Control of a Continuum Manipulator Based on Selective Approach and Koopman Operator

IEEE Transactions on Industrial Electronics

10.1109/TIE.2023.3236082

http://dx.doi.org/10.1109/tie.2023.3236082

Haodong Wang, Wenyu Liang, Boyuan Liang, Hongliang Ren, Zhijiang Du, Yan Wu

Electrical and Electronic Engineering, Control and Systems Engineering

17 January 2023

Wang, H., Liang, W., Liang, B., Ren, H., Du, Z., & Wu, Y. (2023). Robust Position Control of a Continuum Manipulator Based on Selective Approach and Koopman Operator. IEEE Transactions on Industrial Electronics, 70(12), 12522–12532. https://doi.org/10.1109/tie.2023.3236082

Continuum manipulators have infinite degrees of freedom and high flexibility, making it challenging for accurate modeling and control. Some common modeling methods include mechanical modeling strategy, neural network strategy, constant curvature assumption, etc. However, the inverse kinematics of the mechanical modeling strategy is difficult to obtain while a strategy using neural networks may not converge in some applications. For algorithm implementation, the constant curvature assumption is used as the basis to design the controller. When the driving wire is tight, the linear controller under constant curvature assumption works well in manipulator position control. However, this assumption of linearity between the deformation angle and the driving input value breaks upon repeated use of the driving wires which get inevitably lengthened. This degrades the accuracy of the controller. In this work, the Koopman theory is used to identify the nonlinear model of the continuum manipulator. Under the linearized model, the control input is obtained through model predictive control (MPC). As the lifted function can affect the effectiveness of the Koopman operator-based MPC (K-MPC), a novel design method of the lifted function through the Legendre polynomial is proposed. To attain higher control efficiency and computational accuracy, we use a selective control scheme according to the state of the driving wires. When the driving wire is tight, the linear controller is employed; otherwise, the K-MPC is adopted. Finally, a set of static and dynamic experiments have been conducted using an experimental prototype. The results demonstrate high effectiveness and good performance of the selective control scheme.

Publisher Copyright

This research / project is supported by the A*STAR - Robotic Horizontal Technology Coordinating Office Seed Fund
Grant Reference no. : C211518005

This research is supported by the National Natural Science Foundation of China under Grant No. U1813213, the Hong Kong Research Grants Council (RGC) Collaborative Research Fund under grant No. CRF C4026-21GF, the China Scholarship Council under grant No. 202106120121,

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