What can be done with an uncalibrated stereo system?

Over the last several years, there has been an increasing appreciation of the impact of control architecture on the accuracy of visual servoing systems. In particular, it is generally acknowledged that so-called image-based methods provide the highest guarantees of accuracy on inaccurately calibrated hand-eye systems. Less clear is the impact of the control architecture on the set of tasks which the system can perform. In this article, we present a formal analysis of control architectures for hand-eye coordination. Specifically, we first state a formal characterization of what makes a task performable under three possible encoding methods. Then, for the specific case of cameras modeled using projective geometry, we relate this characterization to notions of projective invariance and demonstrate the limits of achievable performance in this regard.