This paper concerns the stability analysis of a new vision-based control which is invariant to camera intrinsic parameters. The necessary and sufficient conditions for the local asymptotic stability show that the control law is robust in the presence of large calibration errors. Local stability implies that the system can accurately track a path in the invariant space. Even if the camera is uncalibrated, the path can be chosen such that the camera follows a straight line in the Cartesian space. Simple sufficient conditions are given in order to keep the tracking error bounded.