Visual Servoing of Rigid-Link Flexible-Joint Manipulators in the Presence of Unknown Camera Parameters and Boundary Output

Exact position control of the flexible-joint manipulator (FJM) is a challenging task due to the manipulator's nonlinearity and underactuated characteristic. For the three-dimensional (3-D) rigid-link FJM, the image-based visual servoing (IBVS) approach with link-position output constraint and unknown camera parameters is investigated in this article. The controller is designed to deal with three problems. First, the visual servoing control law is divided into two domains based on the singular perturbation method, where the control input for the fast subsystem is developed to damp out the flexible joint's vibration. Second, the adaptive updating law for estimating the unknown camera parameters is presented in the slow subsystem. Third, to guarantee that the rigid-link position keep in set constraints, the controller for the slow subsystem is designed by introducing a barrier Lyapunov function. According to the Lyapunov theorem of stability, the proposed controller for the FJM is theoretically proved to be asymptotically stable. Several numerical simulation experiments are provided to illustrate that the presented control scheme is effective.