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This paper presents a novel adaptive controller for image-based visual servoing of robots with an uncalibrated eye-in-hand camera using line features. The controller is developed based on three key ideas. First, we propose a new method that is similar to the Plucker coordinates, to represent projections of the lines features. The new representation leads to a depth-independent image Jacobian matrix and an error vector between real images and estimated projections of the lines, which are both linear to the unknown camera parameters. Second, an adaptive algorithm is developed to estimate the unknown camera parameters and the 3-D coordinates of the lines on-line. Third, a simple controller using the depth-independent image Jacobian is designed to control the projections of the lines to desired positions and orientations. The Lyapunov theory is used to prove the asymptotic convergence of the image error to zero based on the nonlinear robot dynamics. Finally, experiments have been conducted to demonstrate the performance of the proposed approach.