Camera Intrinsic Invariance of Image Jacobian in 4 DOF Image Based Visual Servo

In the image based visual servo, image Jacobian is vital to the system performance because it is the bridge that warps the velocity in feature space to camera velocity in Cartesian space. However, image Jacobian is sensitive to the camera intrinsic parameters, while the camera intrinsic parameter calibration error is almost unavoidable, which heavily affects the image Jacobian and visual servo process. In this paper, we find the camera intrinsic parameter invariance of the image Jacobian in our 4 DOF visual servo system. The image Jacobian of some geometry features is invariant to the camera intrinsic parameters, indicating that the disturbance in camera intrinsic parameters will not affect the convergence trajectory of those features. To further analyse camera intrinsic invariance, we proposed camera intrinsic parameter Jacobian of Image Jacobian, which can fully describe the camera intrinsic parameter invariance of the image Jacobian. The work in this paper can be used to analyse the system sensitivity to the camera intrinsic parameters. The camera intrinsic invariance is also significant for choosing the visual servo features when designing the visual servo system.