Visual Servoing and Pose Estimation with Cameras Obeying the Unified Model - Visual Servoing via Advanced Numerical Methods - page 223

unpredictable when the visual features are not adequately chosen. Furthermore,
other problems may appear such as reaching local minimum or a task singularity
[5]. A compromise and an hybrid visual servoing [19] can be obtained by combin-
ing features in image and partial 3D data.
In this chapter, we are concerned with IBVS. In fact, the main cause of trouble
for IBVS is the strong nonlinearities in the relation from the image space to the
workspace that are generally observed in the interaction matrix. In principle, an ex-
ponential decoupled decrease will be obtained simultaneously on the visual features
and on the camera velocity, which would provide a perfect behavior, if the interac-
tion matrix is constant. Unfortunately, that is not usually the case. To overcome the
problem of nonlinearities observed in the interaction matrix, an approach consists
in using the measures to build particular visual features that will ensure expected
properties of the control scheme. In fact, the way to design adequate visual features
is directly linked to the modeling of their interaction with the robot motion, from
which all control properties can be analyzed theoretically. If the interaction is too
complex ( i.e. highly nonlinear and coupled), the analysis becomes impossible. Sev-
eral works have been realized in IBVS following this general objective. In [24], a
vanishing point and the horizon line have been selected. This choice ensures a good
decoupling between translational and rotational degrees of freedom (DOF). In [15],
vanishing points have also been used for a dedicated object (a 3D rectangle), once
again for decoupling properties. For the same object, six visual features have been
designed in [6] to control the 6 DOF of a robot arm, following a partitioned ap-
proach. In [14], 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 [13], the three coordinates of the centroid of an object in a virtual image obtained
through a spherical projection have been selected to control 3 DOF of an under-
actuated system. Recently, [11] proposed a decoupled visual servoing from spheres
using a spherical projection model. Despite of the large quantity of results obtained
in the last few years, the choice of the set of visual features to be used in the con-
trol scheme is still an open question in terms of stability analysis and validity for
different kinds of sensor and environment.
In this chapter, invariants computed from the projection onto the surface of the
unit sphere will be used to improve the IBVS behavior in terms of convergence
domain and 3D behavior. In previous works, the invariance property of some com-
binations of image moments computed from image regions or a set of points have
been used to decouple the DOF from each-other. For instance, in [28, 30], moments
allow using of intuitive geometrical features, such as the center of gravity or the
orientation of an object. However, these works only concerned planar objects and
conventional perspective cameras. More recently, a new decoupled IBVS from the
projection onto the unit sphere has been proposed in [31]. The proposed method is
based on polynomials invariant to rotational motion computed from a set of image
points. This current work improves the proposed features given in [31]. More pre-
cisely, the new features allow obtaining interaction matrices almost constant with
respect to the depth distributions. This decreases the system nonlinearity and im-
proves the convergence speed and rate.