Handling discontinuities in stereovisual alignment tasks

For more than a decade the capabilities of incompletely calibrated stereo systems have been formally characterized. These characterizations provide theoretical limits on the tasks that visually guided robotic systems can achieve. Within these limits there are several feature-alignment tasks whose image-space representations are inherently discontinuous, including collinearity and coplanarity. This paper presents smooth, locally convergent image-space approximations for such tasks. In addition, we propose the general notion of a "safe" image-based approximation to spatial tasks, in which complete image-space characterization is sacrificed in return for partial characterization along with local controllability. As a result, this article bridges the gap between theoretically specifiable tasks and locally controllable tasks for common stereovisual servoing systems.