Research Article

Delay-Dependent Stability in Uncalibrated Image-Based Dynamic Visual Servoing Robotic System

Table 2

List of notations and symbols.

Notationsā€‰
Perspective projection matrix
Homogeneous transformation matrix from the end effector to the base
Rotation matrix included in
Translation vector included in
Homogeneous transformation matrix from the camera to the end effector
The Cartesian coordinates of the feature point w.r.t. the robot base frame
The matrix consists of the left part of
The 1st and 2nd rows of
The 3rd row of
Jacobian matrix
The inertia matrix of manipulator dynamics
The Coriolis and centrifugal forces
The gravitational force
The control input
The depth-independent Jacobian matrix
The vector derived from
The delay-affected depth-independent Jacobian matrix
A novel composite Jacobian matrix
, The control gain matrices
, The regressor matrices
The unknown parameter vector
, the column vector whose th element is 1 and the other element is 0
, the row vector whose th element is 1 and other elements are 0

Symbolsā€‰
The standard Euclidean norm
The transposition of matrix
The matrix consists of the minimum elements of
The matrix consists of the maximum elements of
The element in the th row and the th column of matrix
The visual signal delayed unknown constant duration of