2 . 5 D Visual Servoing with a Fixed Camera 1

In this paper, we investigate the translational and rotational motion of the end-effector of a robot under visual feedback from a Þxed camera. We achieve an exponential stability result for the regulation of the end-effector to a desired location and orientation. SpeciÞcally, by utilizing visual information from one Þxed camera, we capture the motion of 4 points located in a Þctitious plane attached to the end-effector of the robot that allows us to set up the control problem for the 6 −DOF motion of the end-effector in Cartesian space. By assuming knowledge of the camera intrinsic parameters, we obtain the rotational motion of the end-effector through a homography decomposition while utilizing the pixel motion of one of the four points to obtain the translation information. The stability of the controller is proven through a Lyapunov-based stability analysis.

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