Path-Planning for Visual Servoing: A Review and Issues - Visual Servoing via Advanced Numerical Methods - page 185

Singularities in image Jacobian . At these singularities, certain camera motions
cannot be achieved by the motion of image features in the image space. Several
cases of image singularities have been considered in [6]: the image Jacobian s L x
is known to be singular if the vector of image features s consists of the image of
(1) three collinear points, or (2) three points belonging to a cylinder containing
the camera optical center. Although using more than three noncoplanar points will
avoid such singularities, the image Jacobian may still become singular no matter
how many feature points (irrespective of their arrangements) are used to define the
task function. For example, a visual servoing task involving a 180 degrees rotation
around the optical axis results in a singular image Jacobian. As shown in [6] using
line features instead of points helps to avoid such singularities, however, it does not
completely eliminate the singularities in the image space. Motion perceptibility [59]
has been proposed as a measure of closeness to image singularities.

11.2.2 Robot/Physical Constraints

Motion of the robot/camera system induced by the visual servo control loop, es-
pecially in IBVS, may also violate certain constraints imposed by the robot and/or
physical obstacles in the workspace. These are: (1) robot kinematics such as joint
limits and singularities in robot Jacobian, (2) robot dynamics ,(3) collision with
obstacles or self-collision, and (4) occlusion due to obstacles, robot body, or self-
occlusion by the target.
Over the past three decades a great deal of research in robotics community has
been devoted to planning feasible paths avoiding robot kinematics and/or dynamics
constraints and collision with physical obstacles or self-collision in various envi-
ronments (see e.g. [39] and [40]). Path-planning approaches have also considered
occlusion constraints in applications that require target visibility, e.g. [41] and [51].
Since Chaumette's article [6] on the convergence and stability problems of clas-
sical visual servoing techniques, most of the efforts in visual servoing community
have been devoted to taking the above image/camera and/or robot/physical con-
straints into account and incorporating them into the reactive visual servoing control
loop.
First a number of researchers proposed partitioned (or decoupled) control
schemes in which certain degrees of freedom are controlled in the manner of IBVS
while others are controlled in the manner of PBVS, thereby taking advantage of
each individual technique's benefit in avoiding some of the above constraints (see
e.g. [16], [18], [44], [47], [52]). Each of these partitioned approaches has its own
benefits and drawbacks in accounting for the aforementioned constraints. A perfor-
mance test has been presented in [25] comparing the efficiency of some of the above
partitioned strategies with IBVS technique.
Later on, inspired by the theory of hybrid systems, a number of researchers pro-
posed hybrid (or switched) strategies consisting a set of visual servo controllers
along with a switching rule to switch between them if required (see e.g. , [11], [19],
[24], [27]). Using switched strategies it might be possible to enlarge the stability