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Ta b l e 2 . 3
Error measurements for the fifty rigid body rotation experiments
Average Error σ Error Max Error Min Error
0
.
0391
◦
0
.
0257
◦
0
.
1277
◦
2
.
2192
×
10
−
6
◦
θ
1
0
.
0417
◦
0
.
0314
◦
0
.
1175
◦
6
.
18
×
10
−
4
◦
θ
2
0
.
0474
◦
0
.
0463
◦
0
.
2649
◦
0
.
0017
◦
θ
3
1
+θ
2
+θ
3
0
.
0853
◦
0
.
0446
◦
0
.
2781
◦
0
.
0151
◦
θ
near the periphery. Since most of our objects and kernels were between these two
extremes, the pixel error was calculated based on pixel motions in this intermediate
region. The structure containing the objects was at a distance such that the relation-
ship between the rotations about the focus of the parabolic mirror and the image
motions was approximately 0
6
◦
/pixel. Referring to Table 2.3 we see that the maxi-
mum error was about one-third of a pixel and the average error was about one-fifth
of a pixel.
.
2.4
Conclusions
The results of the analysis in Section 2.3.1 and experimentation in Section 2.3.2
indicate that relaxing the assumptions required for the analytical treatment of KBVS
does not hamper experimental performance. We achieved adequate convergence rate
and domain of attraction. Moreover, the KBVS results in very low steady-state error,
despite our current
ad hoc
approach to kernel selection.
Robust kernel selection for unstructured environments is an area for future re-
search. Figure 2.3 demonstrated how slight variations in kernel selection could cause
the robot to fail to converge to the goal image. Even though both sets of kernel sat-
isfied the rank requirement for the Jacobian between
˙
and
x
, one choice is clearly
superior with respect to the size of the domain of attraction. The ability to optimize
kernel selection to maximize the domain of attraction using only the image at the
goal is the natural next step.
ξ
References
[1] Chaumette, F., Hutchinson, S.: Visual servo control, part ii: Advanced approaches.
IEEE Robotics and Automation Magazine 14(1), 109-118 (2007)
[2] Chaumette, F., Malis, E.: 2 1/2 D visual servoing: a possible solution to improving
image-based and position based visual servoings. In: IEEE International Conference
on Robotics and Automation (2000)
[3] Collewet, C., Marchand, E., Chaumette, F.: Visual servoing set free from image pro-
cessing. In: IEEE International Conference on Robotics and Automation, pp. 81-86
(2008)
[4] Comaniciu, D., Ramesh, V., Meer, P.: Kernel-based object tracking. IEEE Transactions
on Pattern Analysis and Machine Intelligence 25(5), 564-575 (2003)
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