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This paper presents a novel visual servoing strategy for a nonholonomic mobile robot, which is based on a new motion estimation technique. By taking into account the planar motion constraint of mobile robots, the proposed motion estimation technique does not require the estimation and decomposition of the homography or fundamental matrix, and it dose not cause any ambiguity problems. Moreover, the camera field-of-view (FOV) constraint and the partial occlusion problem are largely alleviated because the presented algorithm works well with few feature points. In order to incorporate the advantages of position-based visual servoing (PBVS) and image-based visual servoing (IBVS), a novel hybrid error vector is defined including both image signals and the estimated rotational angle. Furthermore, a smooth time-varying feedback controller is adopted to cope with the nonholonomic constraints, which yields global exponential stability for the closed-loop system despite the lack of depth information. Simulation results demonstrate the performance of the proposed approach.