The Resolvability Ellipsoid for Sensor Based Manipulation

This paper presents a new sensor placement measure calledresolvability. 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 termresolvability refers to the ability of a visual sensor to resolve object positions and orientations. Our main interest inresolvabilityis in determining the accuracy with which a manipulator being observed by a camera can visually servo an object to a goal position and orientation. Theresolvabilityellipsoid is introduced to illustrate the directional nature ofresolvability, 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 thatresolvabilitycan be used to direct camera-lens motion in order to increase the ability of a visually servoed manipulator to precisely servo objects.