Uncalibrated Visual Servoing for a Planar Two Link Rigid-Flexible Manipulator Without Joint-Space-Velocity Measurement

In this article, to solve trajectory tracing problem and vibration suppression for a planar two-link rigid-flexible manipulator subject to joint-velocity measurement noise, a novel uncalibrated visual servoing control is proposed. To begin with, the manipulator's dynamic model is established by the assumed mode method (AMM). On this basis, based on the singular perturbation theory, two subsystem controllers are designed, one is slow subsystem controller, and the other one is fast subsystem controller. In the slow subsystem, to cope with the complication of the camera calibration, an adaptive algorithm is formulated to evaluate the parameters of a fixed camera online. Aiming to overcome the challenge that exact joint-velocity measurement may be disturbed by external noise, a nonlinear sliding observer is developed to estimate the state of joint velocity accurately. The asymptotic convergence of image tracking error is proved by means of Lyapunov analysis. Additionally, for the purpose of restraining the flexible beam's elastic vibration, a linear quadratic regulator (LQR) approach is adopted in the fast subsystem control design. The realistic comparing simulation experiments are presented to demonstrate the performance of the proposed controller.