Decidability of robot positioning tasks using stereo vision systems
João P. Hespanha, Zachary Dodds, Gregory D. Hager, A. Stephen Morse · 2002
Conditions are given which enable one to decide on the basis of images of point features observed by an imprecisely modeled two-camera stereo vision system, whether or not a prescribed robot positioning task has been accomplished with precision. It is shown that for a stereo vision system whose two-camera model is known only up to a projective transformation, one can decide with the available data whether or not such a positioning task has been accomplished, just in case the function which specifies the task is a projective invariant. It is then shown that, under suitable technical conditions, every task with this property can be constructed from primitive tasks by using only a small number of distinct operations.