Luminance: A New Visual Feature for Visual Servoing - Visual Servoing via Advanced Numerical Methods - page 77

5.4 Experimental Results

In all the experiments reported here, the camera is mounted on a 6 DOF gantry robot.
Control law is computed on a Core 4 2 Duo 3 GHz PC running Linux 5 .Imagesare
acquired at 66 Hz using an IEEE 1394 camera with a resolution of 320

×

240.
The size of the vector s is then 76800. Despite this size, the interaction matrix L I
involved in (5.36) can be computed at each iteration if needed.

5.4.1 Positioning Tasks under Temporal Luminance Constancy

We assume in this section that the temporal luminance constancy hypothesis is valid.
To make this assumption as valid as possible, a diffuse lighting as been used so
that I ( x ) can be considered as constant with respect to to the viewing direction.
Moreover, the lighting is also motionless with respect to the scene being observed.
In this section, we will first compare the GN and MLM methods and then show that
the photometric visual servoing is robust.

5.4.1.1 Comparison between the GN and the MLM Methods

The goal of the first experiment is to compare the control laws based on GN and
MLM approaches when a planar object is considered (it is a photo). The initial error
pose was r init =(5 cm, -23 cm, 5 cm, -12.5 deg, -8.4 deg, -15.5 deg ). The desired

pose was so that the object and charge-coupled device (CCD) planes are parallel
at Z = Z ∗ = 80 cm. The interaction matrix has been computed at each iteration but
assuming that all the depths are constant and equal to Z ∗ , which is of course a coarse
approximation.
Figure 5.3(a) depicts the behavior of cost functions using the GN method or the
MLM method while Figure 5.3(b) depicts the trajectories (expressed in the desired
frame) when using either the GN or the MLM method. Figures 5.3(c-d) depict re-
spectively the translation errors for the GN and MLM method while Figures 5.3(e-f)
depict respectively the orientation errors for the GN and MLM method. The initial
and final images are reported respectively on Figures 5.3(g-h). First, as it can be
seen on Figure 5.3(a), both the control laws converge since the cost functions vanish.
However, the time-to-convergence with the GN method is much higher than the one
of the MLM method. The trajectory when using the GN method is also shaky com-
pared to the one of the MLM method (Figure 5.3(b)). Compare also Figure 5.3(c)
with Figure 5.3(d) and Figure 5.3(e) with Figure 5.3(f). The velocity of the camera
when using the MLM method is smoother than when using the GN method (Fig-
ure 5.3(d) and Figure 5.3(c)). This experiment clearly shows that the MLM method
outperforms the GN one. Note that in both cases the positioning errors is very low,
for the MLM method we obtained

Δ

Δ r =(0.26 mm, 0.30 mm, 0.03 mm, 0.02 deg,

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http://www.intel.com

4

5

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