Information Technology Reference
In-Depth Information
are neither physically valid nor optimal due to the nonlinearity and singularities in
the relation from the image space to the workspace [1].
Dealing with this deficiency, an approach consists on selecting features with good
decoupling and linearizing properties. In [18], vanishing points have been used for
a dedicated object (a 3D rectangle), to obtain some decoupling properties. For the
same object, six visual features have been designed in [7] to control the 6 degrees
of freedom (DOF) of a robot arm, following a partitioned approach. In [17], the
coordinates of points are expressed in a cylindrical coordinate system instead of
the classical Cartesian one, so as to improve the robot trajectory. In [14], the three
coordinates of the centroid of an object in a virtual image obtained through a spher-
ical projection have been selected to control 3 DOF of an under-actuated system.
In [19], Mahony
et al.
deals with the selection of the optimal feature to control the
camera motion with respect to the depth axis. Tatsambon
et al.
in [12] proposed a
decoupled visual servoing from spheres using a spherical projection model. In [9],
translational and rotational motions are decoupled by using the homography and
the epipolar constraint between the current and the goal images. In [27], moments
in the unit sphere allow to design partitioned systems with good decoupling and
linearizing properties.
An other approach consists on coupling path-planning method to image-based
servoing. Indeed, if the initial error is too large, a reference trajectory can be de-
signed from a sequence of images. The initial error can thus be sampled so that, at
each iteration of the control loop, the error to regulate remains small. In [15], relay
images that interpolate initial and reference image features using an affine approxi-
mation of the relationship between initial and desired images, coupled to a potential
switching control scheme, is proposed to enlarge the stable region. In [16], a trajec-
tory generator using a stereo system is proposed and applied to obstacle avoidance.
An alignment task for an 4 DOF robot using intermediate views of the object syn-
thesized by image morphing is presented in [26]. A path-planning for a straight-line
robot translation observed by a weakly calibrated stereo system is performed in
[25]. In [22], a potential field-based path-planning generator that determines the tra-
jectories in the image of a set of points lying on an unknown target is presented.
To increase the stability region, [8] describes a globally stabilizing method using
navigation function for eye-to-hand setup while in [6], the authors propose to use
circular-like trajectories. In [5], the camera is constrained to follow a straight line
while ensuring visibility.
However, none of these works were dealing with optimality issues. In [29], a
numerical framework for the design of optimal trajectories in the image space is
described and applied to the simple case of a one dimensional camera in a two di-
mensional workspace. In [23] an analytical solution to none-constrained optimal
path-planning in the image space for general setup is presented. In this chapter, we
address the problem of generating trajectories of image features that corresponds
to optimal 3D trajectories under visibility constraints in order to control efficiently
a robotic system using an image-based control strategy. First, a collineation path
between given start and end points is obtained and then the trajectories of the im-
age features are derived. Path planning is formulate as a variational problem which
Search WWH ::
Custom Search