The Resolvability Ellipsoid for Visual Servoing

This paper introduces a sensor placement measure called resolvability. The measure provides a technique for estimating the relative ability of various visual sensors, including monocular systems, stereo pairs, multi-baseline stereo systems, and 3D rangefinders, to accurately control visually manipulated objects. The resolvability ellipsoid illustrates the directional nature of resolvability, and can be used to direct camera motion and adjust camera intrinsic parameters in real-time so that the servoing accuracy of the visual servoing system improves with camera-lens motion. The Jacobian mapping from task space to sensor space is derived for a monocular system, a stereo pair with parallel optical axes, and a stereo pair with perpendicular optical axes. Resolvability ellipsoids based on these mappings for various sensor configurations are presented. Visual servoing experiments demonstrate that resolvability can be used to direct camera-lens motion in order to increase the ability of a visually servoed manipulator to precisely servo objects.