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While PBVS methods are the most straightforward ones, they require metrical
information about the feature positions, usually organized in a map . When the met-
rical information can't be computed directly from the camera view (which is the
case for a monocular camera), pose estimation is usually achieved with the addi-
tional use of external measurements, such as odometric data. Therefore, the latest
research focuses on hybrid methods or pure IBVS methods to overcome the esti-
mation problem. Among the others, hybrid schemes have been proposed in [11],
coming up to a scheme which is roughly half-way between IBVS and PBVS, and
in [16], where a switched control approach that utilizes both schemes depending on
the distance to the target has been implemented. Indeed, IBVS is more accurate than
PBVS as soon as the reference and the target images are close enough ([4, 5]). For
this reason, an image based task is often separated into a set of consecutive control
problems using a sequence of target images, in other words using appearance-based
visual maps that not take into account any 3D spatial information ([28, 15]).
In the past few years, robot scientists have focused on the optimality of paths
followed by visually servoed robots. For example, researchers have focused on the
optimal control of visually guided robotic manipulators ([8]) or on optimal trajec-
tory planning for robot manipulators controlled via a limited FOV camera ([13]).
Minimal trajectories have been also presented in [25] in case of large displace-
ments, again for a six degrees of freedom robot manipulator. Optimal paths for
differentially driven robots with visibility restricted to limited FOV have recently
been addressed by some researchers ([2, 30]). The solutions proposed in this field
are more related to optimal path planning than robot reactive control, restricting the
role of the visual control to path following. Of course, also in this case solutions can
be divided in position based or image based, depending on the space in which the
trajectories are derived.
In this chapter we aim to provide an overview to the visual servoing of differen-
tially driven robot and the vision theoretic fundamentals needed in each case. Then,
a PBVS control scheme that solves the problem in the 3D domain is proposed,
together with a servoing-oriented simultaneous localization and mapping (SLAM)
algorithm to enhance the potentiality of the controller. To overcome the localiza-
tion process, a combination of an IBVS and an optimal (shortest) path planner is
then proposed. Again, the autonomous capability of the servoed robot are increased
adopting an appearance map-based approach. A discussion on the advantages and
drawbacks that pertain to each technique is also presented.
18.2
Problem Definition
The visual servoing problem as meant in this chapter is referred to mobile vehicles,
with a rigidly fixed on-board camera. In particular, we consider vehicles that con-
stantly move on a plane, as in typical indoor set-up, like factory or office floors.
We assume for the moving platform a driftless kinematic model, more precisely this
chapter refers to a unicycle-like nonholonomic mobile robot. Without loss of gener-
ality, we assume that the robot coordinates are measured with respect to a dextrous
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