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

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.