1.2 State of the Art on Visual Control 7
control purposes: the homography model, the epipolar geometry and the trifocal
tensor. The use of geometric constraints has given origin to hybrid schemes that
improve the performance of classical image-based visual servoing. In [48], the ho-
mography and the epipolar constraint are used to generate the optimal trajectory of
the robot motion to reach the goal straightforwardly with decoupled translation and
rotation. The 2-1/2D visual servoing which is based on the estimation of the partial
camera displacement from the current to the desired camera poses at each iteration
of the control law is proposed in [96]. This scheme does not need any geometric 3D
model of the object as required in position-based visual servoing, and it ensures the
convergence of the control law in the whole task space, unlike image-based visual
servoing. An outstanding work in the hybrid visual control approach concerns about
the stability analysis of a class of model-free visual servoing methods that can be
hybrid or position-based visual servoing [95]. In any of both cases, these methods
do not need a 3D model of the target object. Additionally, the visual servoing is
decoupled by controlling the rotation of the camera separately from the rest of the
system. In [34], a homography-based adaptive visual servo controller is developed
to enable a robot end-effector to track a desired Euclidean trajectory as determined
by a sequence of images. The error systems are constructed as a hybrid of pixels in-
formation and reconstructed Euclidean variables obtained by comparing the images
and decomposing a homographic relationship.
A homography-based approach for image-based visual tracking and servoing is
proposed in [23]. The visual tracking algorithm is based on an efficient second-order
minimization method and its output is a homography linking the current and the ref-
erence image of a planar target. Using the homography, a task function isomorphic
to the camera pose is designed, and thus, an image-based control law is proposed. In
[35], an image-space path planner is proposed to generate a desired image trajectory
based on a measurable image Jacobian-like matrix and an image-space navigation
function. An adaptive homography-based visual servo tracking controller is then de-
veloped to navigate to a goal pose along the desired image-space trajectory while
ensuring that the target points remain visible.
In order to avoid the largely over-constrained control commands resulting in
monocular approaches, in [75], the authors propose to exploit explicitly the epipolar
constraint of two stereo images. A hybrid switched-system visual servo method that
utilizes both image-based and position-based visual servoing is presented in [54].
The switching strategy achieves stability in both the pose space and image space si-
multaneously. With this strategy is possible to specify neighborhoods for the image
error and pose error that the state can never leave. In [13], the epipolar constraint is
introduced for visual homing of robot manipulators. By using the epipolar geome-
try, most of the parameters (except depth) which specify the differences in position
and orientation of the camera between the current and target images are recovered.
The method is memoryless, in the sense that at every step the path to the target po-
sition is determined independently of the previous path. In [118], a visual servoing
based on epipolar geometry for manipulators is reported. It discusses how the real
value of the translation to be reached is unpredictable and proposes a control scheme
which decouples the control of the rotation and the translation using the projective