Path-Planning for Visual Servoing: A Review and Issues - Visual Servoing via Advanced Numerical Methods - page 184

categorization based on the underlying path-planning techniques are provided. In
Section 11.4 we discuss the effect of uncertainties on visual servoing and report on
some recent works aimed at path-planning under uncertainty for visual servoing.
Finally, we conclude the survey in Section 11.5.

11.2 Constraints in Visual Servoing

In [6], through simple, yet, effective examples, Chaumette outlined the potential
problems of stability and convergence in both IBVS and PBVS techniques imposed
by a number of constraints. Overall one can divide these constraints into two main
categories: (1) image/camera, and (2) robot/physical constraints. These two cate-
gories are detailed as follows.

11.2.1 Image/Camera Constraints

The image/camera constraints are mainly due to the sensing limits of the vision
system or the inter-relationship between the optical flow ( i.e. , rate of change) of
the features s

k n

∈ R in the image space and the camera's Cartesian velocity x ∈ R

k × n

s L x ∈ R

defined through the image Jacobian (also called interaction matrix)

related to image features [31]:

s = s L x x

(11.2)

These constraints are: (1) field of view limits ,(2) image local minima ,and(3) sin-
gularities in image Jacobian .
Field of view limits . The camera as a sensing system have certain limitations.
For example the 3D target features projected into the image plane of the camera are
visible if their projections fall inside the boundary of the image. The limits of the
image are usually represented by a rectangular region which determines the visible
region of the image plane. Although in IBVS context the control is directly defined
in the image, there is still the possibility that the features leave the camera's field of
view, in particular when the initial and desired poses of the camera are distant [6].
Image local minima . As shown in [6], in IBVS context, image local minima might
occur due to the existence of unrealizable image motions which do not belong to the
range space of image Jacobian s L x . Hence, there does not exist any camera motion
able to produce such unrealizable motions in the image. In general, determining
the image local minima is difficult without considering the specific target location
and the initial and desired relative camera-target locations, which in turn, leads to
an exhaustive search for local minima in the image for each instance of a visual
servoing task. As demonstrated in [6], using a nominal value of image Jacobian
estimated at the desired location might be of help to avoid local minima in visual
servoing tasks. But this may lead to peculiar trajectories of features in the image,
which in turn, might violate field of view limits. One should note that the PBVS
techniques are known to be free of image local minima since the task function is
defined in the Cartesian space.