Points-based Visual Servoing with Central Cameras - Visual Servoing via Advanced Numerical Methods - page 295

(a) (b)

4

0.08

2

0.06

0

0.04

−2

0.02

−4

0

−6

−0.02

−8

−0.04

−0.06 −10

200 400 600 800 1000 1200 1400 200 400 600 800 1000 1200 1400

(c) (d)

0.2

0.15

0.1

0.05

0

−0.05

200 400 600 800 1000 1200 1400

(e)

Fig. 16.3 A , 2D points-based visual servoing: (a) initial image; (b) desired image and image-
points trajectories; (c) translational velocities in m / s ; (d) rotational velocities in deg / s ;and
(e) error vector components

fails, the robot reaching quickly its joint limits. The rotation about the Z -axis is thus
reduced to 40 deg for the control A .
Figure 16.3 shows the results obtained using the control A . The interaction ma-
trix depends on 3D parameters, points coordinates and calibration parameters. If one
supposes that the camera-robot system is correctly calibrated and that the measure-
ments are noiseless, the 3D parameters should be accurately estimated to guarantee
a quasi-exponential decreasing of the task function e (leading to straight line tra-
jectories of the points in the image plane). In this experiment, the 3D parameters