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166 Autonomous Mobile Robots

deduced, the localization can be done by the transformation

W W L
P = C · P (4.21)
L
The problem now is to calculate

L L L L T
P = (x , y , θ ) (4.22)
c
c
c
In this section, two methods of localization, that is, triangulation, and least
square estimation (LSE), are investigated in terms of two cases: single landmark
and double landmarks.
4.4.2.1 Triangulation method

Figure 4.8 is the sketch map of landmark imaging, using a pinhole model. P1
and P2 are two of the vertical edges of the five characters (10 edges alltogether).
L
L
The positions of P1 and P2 are known as (p ,0) and (p ,0). The parameters of
1 2
the landmark are shown in Figure 4.5a.
According to the pinhole model, we get:
I
I
I
I
(y − y )r H (y − y )r H
2 1 4 3
= and = (4.23)
f l 1 f l 2
I
I
where r is the resolution with the unit of MPD (millimeters per dot), and (x , y )
i i
is the coordinate value of the ith feature point, both endpoints of the selected
vertical edges.
X L u P1 P2
1 O L
y L

l 1
l 2

f X I
2
Lens center

FIGURE 4.8 Landmark detection.

© 2006 by Taylor & Francis Group, LLC

FRANKL: “dk6033_c004” — 2006/3/31 — 16:42 — page 166 — #18