  A gaze-fixating robot perceives distance to the fixated object and relative
positions of surrounding objects immediately, accurately, and robustly. We show
how fixation, which is the act of looking at one object while moving, exploits
regularities in the geometry of 3D space to obtain this information. These
regularities introduce rotation-translation couplings that are not commonly
used in structure from motion. To validate, we use a Franka Emika Robot with an
RGB camera. We a) find that error in distance estimate is less than 5 mm at a
distance of 15 cm, and b) show how relative position can be used to find
obstacles under challenging scenarios. We combine accurate distance estimates
and obstacle information into a reactive robot behavior that is able to pick up
objects of unknown size, while impeded by unforeseen obstacles. Project page:
https://oxidification.com/p/one-object-at-a-time/ .
