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characteristics may provide a benefit over traditional position-based and image-
based visual servoing [10], 2 1/2 D visual servoing [2], and other advanced visual
servo algorithms [1].
“Featureless” visual servoing methods including KBVS take advantage of the
rich set of visual data present in images without reducing the image to feature points.
This reduces computation because extracting image features usually requires more
computation than the image measurements used in featureless methods. Also, this
confers robustness to region or feature occlusions in the images.
Nayar et al. [15] present one of the earliest works in featureless visual servoing.
The authors select patches of the goal image that form a high dimensional mea-
surement. They then generate a training data set of images acquired at known robot
poses. The leading principal components of the training images form a low dimen-
sional approximation of the so-called appearance manifold. Images during control
are projected onto this manifold and control is performed on this low dimensional
space. The sampling of the camera workspace becomes prohibitively time consum-
ing as the number of degrees of freedom increases and has to be evaluated for each
scene. Deguchi [6] extends the method to 6 degrees of freedom and automates patch
selection to improve the Jacobian. These papers do not address formal guarantees
of convergence.
More recently, Tahri and Chaumette [16] use moments for determining camera
motions with respect to a goal. They compute the Jacobian relating changes in low-
order image moments to the velocity of the moving camera. The image moments
provide a similar measurement as the KBVS sampling kernel in that they provide a
scalar measurement of the entire image for each type of moment calculation. For-
mally, with an appropriately designed family of kernels, it may be possible to con-
ceive of moment-based visual servoing as a special case of KBVS. The advantages
of KBVS are that selection of kernels with compact (finite) support will minimize
edge effects, and moreover the KBVS approach embraces gray scale images. How-
ever, the image moment solution provides for 6 degree of freedom visual servoing,
a problem not yet solved for KBVS.
A related result by Collewet et al. [3] notes that for a static scene, the time-
varying image is simply a transformed version of the original image, assuming no
occlusions. They develop the Jacobian relating the motion of every pixel in the im-
age to the motion of the camera, thus allowing derivatives of the image signal to
be calculated directly. They then use the time derivative of the image to minimize
a cost function, which in similar to the Lyapunov function as discussed later in this
chapter, if the image is a continuous signal. This approach is analogous to placing a
kernel at every pixel.
KBVS presents a new kind of featureless visual servoing and this chapter presents
the first in-depth empirical evaluation of KBVS. Section 2.2 presents the KBVS al-
gorithm and its conceptual and theoretical underpinnings. Section 2.3 describes the
experiments conducted to evaluate the method and characterize the convergence
properties for several degrees of freedom. We conclude by discussing the outstand-
ing issues that need to be addressed to make KBVS robust and to rationalize kernel
selection.
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