Decidability of robot positioning tasks using stereo vision systems

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.