Iterative Learning Control for Visual Servoing with Unknown Homography Matrix

An iterative learning control scheme for robot planar motion visual servo with an arbitrarily mounted camera is presented in the paper. In our previous work, it has been proved that, when the image plane and the motion plane are parallel with a constant but unknown image Jacobian matrix, an iterative learning control law with a Nussbaum learning gain can be applied to visual servoing for trajectory tracking without camera calibration. How to design a visual servoing controller for an arbitrarily mounted camera, in which the image Jacobian matrix is shown to be time varying, remains to be an open problem. By utilizing the features of planar homography, the time-varying image Jacobian can be factorized as a constant transformation matrix and a time varying depth. As the time varying depth is bounded, an iterative learning control with a Nussbaum gain is proved to be convergent for planar trajectory tracking under control of an arbitrarily mounted camera.