The Resolvability Ellipsoid for Sensor Based Manipulation

This paper presents a new sensor placement measure called resolvability. This measure provides a technique for estimating the relative ability of various sensor systems, including single camera systems, stereo pairs, multi-baseline stereo systems, and 3D rangefinders, to accurately control visually manipulated objects. The measure also indicates the capability of a visual sensor to provide spatially accurate data on objects of interest. The term resolvability refers to the ability of a visual sensor to resolve object positions and orientations. Our main interest in resolvability is in determining the accuracy with which a manipulator being observed by a camera can visually servo an object to a goal position and orientation. The resolvability ellipsoid is introduced to illustrate 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 single camera 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.