Gradient Projection Methods for Constrained Image-based Visual Servo - Visual Servoing via Advanced Numerical Methods - page 258

distance

50

45

40

35

30

25

20

15

10

5

0

0 5 10 15 20

Fig. 14.11 Distance between the occluding point and target with occlusion avoidance

14.4.2 Simulation Results

These simulations use the same setup as described in Section 14.3.2. We place an
object in the work space, and consider the possibility of occlusion of the first image
feature by this object. The robot task is to reach a desired position, avoiding the
visual occlusion. The model without considering the visual occlusion is the same
as that in Section 14.3.2. The occluding point is set to be (1.0798 0.0649 0.0852),
expressed in the camera frame. When the robot moves to the target position, the
depth of the occluding point is 0.4248 according to the transform of the robot. The
distance between the occluding point and the target is shown in Figure 14.9 without
taking into account the environment constraints.
As shown on Figure 14.9, the distance decreases until reaching its minimum

0 6 s , and then increases afterward. It illustrates the target comes close

to the occluding object and then is occluded by the object at t = 3

. 0635 at t = 3 .

6 s .Afterthe
visual occlusion, it moves away from the occluding object. Therefore, at t = 3

.

. 6 s

the robot cannot observe the target since the occluding of a static point.
The block diagram with visual occlusion avoidance is given in Figure 14.10.
When considering the visual occlusion, the corresponding distance between occlud-
ing point and the target after adding occlusion avoidance are given in Figure 14.11.
At the beginning, the target moves close to the occluding point as shown previously.
But after it reaches 1.9999 at t = 2

9341 s , the distance jumps to 6 in the next itera-
tion. The force generated by the gradient of the cost function drives the robot away
from the occluding object after it is predicted.
Figures 14.12 and 14.13 show respectively some screen shots taken from the
simulation during the servo, the points trajectory in the image plane, and the error
of the main task. Figure 14.12(a) shows the image when occlusion is predicted at t =
2

.

9341 s , and Figure 14.12(b) is the one when occlusion is avoided. Figure 14.13(a)
shows the decay of the error of the main task. Through zooming in Figure 14.13(a),

.