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This paper presents a novel approach for image-based visual servo of a robot manipulator with an eye-in-hand configuration when the camera parameters are not calibrated and the trajectory of the moving object is not predicted. Firstly, the expression of the image Jacobian matrix for the eye-in-hand configuration, namely extended image Jacobian matrix, is proposed, then an update law is designed to estimate the extended image Jacobian online. Furthermore, a control scheme is presented and the Lyapunov method is employed to prove asymptotic convergence of the image errors. No assumption for the moving objects is needed. Finally, Both simulation and experimental results are shown to support the approach in this paper.