Gradient Projection Methods for Constrained Image-based Visual Servo - Visual Servoing via Advanced Numerical Methods - page 259

snapshots of the eye−in−hand camera at t=2.9341s snapshots of the eye−in−hand camera at t=2.9556s

385 385

occlusion point
target point

occlusion point
target point

380 380

375 375

370 370

365 365

185 190 195 200 205 185 190 195 200 205

(a) (b)

Fig. 14.12 Snapshots of the eye-in-hand camera

error error

120

95

u1−u1d
v1−v1d
u2−u2d
v2−v2d

u1−u1d
v1−v1d
u2−u2d
v2−v2d

90

100

85

80

80

60

75

40

70

65

20

60

0

0 5 10 15 20 0 1 2 3 4 5 6

(a) (b)

Fig. 14.13 Feature points motions

the detailed trajectory of the features error around t = 2 9341 s isshowninFigure

14.13(b). We can see that the error still decreases exponentially, except the sawtooth
around t = 2

.

. 9341 s , which corresponds to the activation of the artificial force.

14.5 Gradient Projection Method for Keeping Target Features

in the Field of View

In this section, we describe how gradient projection methods can be used to keep
target features in the camera field of view throughout the camera motion. Below,
we adopt a cost function proposed in [10], and describe the necessary methods for
exploiting this cost function in a gradient projection framework.

14.5.1 Basic Algorithm Design

One approach to keeping target features in the field of view is to construct a cost
function that takes a value equal to zero when target features are at the image center,