In this paper, we consider the position control problem of nonholonomic mobile robots, i.e., the regulation of mobile robots to a desired position specified by the image position of a feature point onboard the mobile robot, by using visual feedback information from an overhead fixed camera. Many vision-based control approaches have been proposed for motion control of nonholonomic mobile robots, however, they usually assume that exact or approximate knowledge of full/partial intrinsic and/or extrinsic parameters of the camera can be available, and large or even very small errors in these parameters can deteriorate the control performance, reduce the control accuracy, and even affect the system stability. Hence, it is interesting and highly desirable to develop vision-based controllers without depending on the camera parameters, from both control performance and controller implementation perspectives. With this in mind, we propose novel image-based position control schemes for nonholonomic mobile robots completely without knowing the camera parameters. In the proposed schemes, neither accurate nor approximate knowledge about the camera intrinsic and extrinsic parameters is required, and the totally unknown camera can be mounted on the ceiling with an arbitrary pose, which can make the controller implementation very simple and flexible. Experimental results are provided to show the feasibility and effectiveness of the proposed schemes.