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In this paper, we shed new light on position-based visual servoing (VS) by introducing the concept of a 3-D visible set for position-based VS (PBVS), which can serve to play exactly the role of the 2-D visible set, the image plane, for image-based VS. Our 3-D visible set is convex even in the presence of uncertainties in intrinsic and extrinsic parameters of the camera, just as the image plane. Then, we can ensure the field of view (FOV) constraint simply by controlling the camera pose to follow a smooth straight-line trajectory in our 3-D visible set for PBVS, which simply connects two points determined by the initial and desired poses of the camera. In fact, this is, to our best knowledge, the first result in PBVS that has guaranteed theoretically robust global stability under the FOV constraint with respect to uncertainties in intrinsic and extrinsic parameters of the camera as well as in the distance between the camera and the object at the desired pose. Furthermore, our PBVS scheme is computationally simple compared to the prior works. To demonstrate further the validity and practicality of our PBVS scheme, we also present various experimental results using a six-degree-of-freedom robotic manipulator.