Visual Servoing of Flexible-Link Manipulators by Considering Vibration Suppression Without Deformation Measurements

Visual servoing and vibration suppression of spatial flexible-link manipulators with a fixed camera setup are addressed in this article. The singular perturbation method is adopted to decouple the dynamic equations of the flexible manipulator; hence, two subsystems that represent the rigid robot motion and flexible-link vibration are obtained, respectively. Then, for the slow subsystem related to the rigid motion, an image-based controller is designed to converge the image errors with the consideration of compensating for the errors of approximating the Jacobian matrix. For the fast subsystem corresponding to the elastic vibration, to eliminate the requirements of measuring the vibration states, an observer is designed to estimate the fast states and then a feedback controller of the fast subsystem is presented to suppress the vibration of the flexible manipulator by using the estimation values. The closed-loop stabilities of the slow and fast subsystem are both proved by employing the Lyapunov theory. Numerical simulations demonstrate the effectiveness of the proposed controller, which shows that the image errors approach zero with the vibration of the flexible manipulator damped out simultaneously.