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(a)
(b)
2
0
0.05
−2
0
−4
−0.05
−6
−0.1
−8
−0.15
−0.2
−10
−0.25
−12
100
200
300
400
500
600
700
800
900
1000
100
200
300
400
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600
700
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1000
(c)
(d)
0
0.4
0.3
−50
0.2
0.1
−100
0
−0.1
−150
100
200
300
400
500
600
700
800
900
1000
100
200
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(e)
(f)
Fig. 16.5 C , norm-ratio-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
It can be first observed that the three control laws allow to achieve the large
rotation about the Z -axis ( i.e. 140 deg) and that, as expected, a rough estimation of
the parameter
ρ does not affect the system stability. It can be also observed that
the decoupling properties have been significantly improved with respect to the 2D
points visual servoing. Finally, let us note that, in Figure 16.4(b) the trajectory of
the point used to define the 2 1/2 D task function should be a straight line. This is
clearly not observed since once again
ρ
is not correctly estimated.
 
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