## 1 Introduction  
External visual sensors are more effective for the closed-loop control of nonholonomic mobile robots than the dead reckoning of internal sensors which can not achieve precise mobile robot poses because of slippage [1, 2, 3, 4]. Visual servoing directly uses the visual information from the onboard camera to design the controller or to estimate the pose of the mobile robot. Existing works on visual servoing of wheeled mobile robots can be mainly formulated as tracking moving objects [5, 6, 7], tracking given path [8, 9, 10] and regulating toward a set-point [11, 12, 13]. Due to the peculiar nature of nonholonomic mobile robots, the set-point stabilization control of the mobile robot is more challenging than tracking problems. This paper deals with the stabilization problem of a nonholonomic mobile robot equipped with a fixed onboard pinhole camera that has a limited field-of-view. According to [PERSON]'s necessary condition [14], mobile robots can not be stabilized via smooth time-invariant static feedback control which makes the existing manipulator visual servo controllers fail in mobile robots. Thus new nonlinear strategies have been developed, such as discontinuous controllers [15] and time-varying controllers [16]. [PERSON] et al. [11] exploit the epipolar geometry to build the system model and zero the epipoles to align the robot with the goal in a straight line by using an input-output linearizing feedback control law. Then a proportional control law can decrease the translation error in the last stage. [PERSON] et al. [12] utilize the 2D and 3D hybrid method to design a time-varying controller which introduces a sinusoidal function to rebuild the system state. [PERSON] et al. [13] also decompose the homography matrix to get the system states which are used in discontinuous change of coordinates to cope with the nonholonomic constraints of the mobile robot. Furthermore, a pan-tilt camera is used to deal with the vision constraint. All above control strategies do not need any priori 3D knowledge of the scene. However, the camera intrinsic parameters should be precisely calibrated in advance. Consider the mobile robots with an uncalibrated camera, some robust visual servo strategies and self-calibration methods have been reported in [17, 18, 19, 20, 21]. [PERSON] et al. [17] develop the control laws for three class optimal paths by using the entries in the homography matrix, while the optimal paths are generated under both the nonholonomic constraints and the field-of-view constraints [22]. [PERSON] et al. [18] directly use the elements of the homography matrix building the error model, while two linear extended state observers are designed to compensate for the parameter uncertainties arising from the unknown 3D information and intrinsic parameters. [PERSON] et al. [19] propose a three-stage strategy including a rotation pointing to the goal, a straight line movement toward the goal, and a rotation regulating the desired pose. The intrinsic parameters estimated in the first stage are used in the latter two stages. Besides, [PERSON] et al. [20] provide a geometric method for calibration of the camera principle point which uses the theorem that the parallel lines along the camera optical axis will meet in the principle point. This method is robust to radical distortion and the variation of the focal length. [PERSON] et al. [21] design a depth observer to estimate the depth online for regulating the mobile manipulator to desired configuration. This method can be extended to estimate the focal length of the camera. Most visual servoing strategies for nonholonomic mobile robots assume the target remaining in the field-of-view during the regulation process. However, as the limited field-of-view of the pinhole camera, the vision constraint is an ineluctable problem of the mobile robot regulation. [PERSON] et al.