Gradient Projection Methods for Constrained Image-based Visual Servo - Visual Servoing via Advanced Numerical Methods - page 256

1

0.8

0.6

0.4

0.2

0

2

1.5 2

1.5

1

1

0.5

0.5

0

0

Fig. 14.8 Cost function used for visual-occlusion avoidance in the image space

distance

40

35

30

25

20

15

10

5

0

0 5 10 15 20

Fig. 14.9 Distance between the occluding point and target without occlusion avoidance

V occ =

d x e − β d 2 − 2 β

∇ . (14.42)

d y e − β d 2

−

2 β

The artificial force that avoids the occlusions can be now computed using (14.28).
The transformation from the image space to the articular space is given by:

∂Φ
∂

+

r ∂

r

g occ = ∇ Φ V occ = ( L Φ MJ q ) + ∇ Φ V occ

− − , (14.43)

∂ q

where r is the chosen camera pose parametrization, M and J q are the transformation
matrices defined before, and L Φ is the well-known interaction matrix related to the
image point x a .