A novel visual servoing structure is introduced for a 3D robot positioning under an eye-to-hand camera configuration. The proposed algorithm is based upon Image-Based Visual Servoing (IBVS) and uses only one fixed camera in conjunction with a stationary flat mirror. A landmark mounted on the robot's end-effector along with its mirror reflection provide enough information for 3D reasoning based on a 2D image when viewed by a camera. The equations describing the relationship between the robot's velocity and rate of change in image features called the image Jacobian are presented. Moreover, a novel set of image feature points that yield a full-rank image Jacobian is introduced. We present two techniques based on an off-line camera calibration and an on-line estimation of the image Jacobian. By introducing a Kalman filter and the Recursive Least Squares method, camera calibration and knowledge of the workspace are not needed. Simulated and experimental results illustrate the robustness of the proposed visual servoing structure. In addition, the stability and accuracy of each proposed visual servoing algorithm are evaluated with an error analysis and sensitivity tests.
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