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A 2-1/2-D visual servoing strategy, which is based on a novel motion-estimation technique, is presented for the stabilization of a nonholonomic mobile robot (which is also called the “parking problem”). By taking into account the planar motion constraint of mobile robots, the proposed motion-estimation technique can be applied in both planar and nonplanar scenes. In addition, this approach requires no matrix estimation or decomposition, and it avoids ambiguity and degeneracy problems for the homography or fundamental matrix-based algorithms. Moreover, the field-of-view (FOV) constraint of the onboard camera is largely alleviated because the presented algorithm works well with few feature points. In order to incorporate the advantages of position-based visual servoing and image-based visual servoing, a composite error vector is defined that includes both image signals and the estimated rotational angle. Subsequently, a smooth time-varying feedback controller is adopted to cope with the nonholonomic constraints, which yields global exponential convergent rate for the closed-loop system. On the basis of the perturbed linear system theory, we show that practical exponential stability can be achieved, despite the lack of depth information, which is inherent for monocular camera systems. Both simulation and experiment results are collected to investigate the feasibility of the proposed approach.