Page 129 - Introduction to Autonomous Mobile Robots

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a) b Chapter 4

u

fcotα-u
Camera
Laser / Collimated beam
u
b f

x
α Lens
H=D·tanα
z
b)

Target
(x, z)

Transmitted Beam
c) Reflected Beam

Figure 4.15
(a) Principle of active two dimensional triangulation. (b) Other possible light structures. (c) 1D sche-
matic of the principle. Image (a) and (b) courtesy of Albert-Jan Baerveldt, Halmstad University.

sured values in the system are α and u, the distance of the illuminated point from the origin
in the imaging sensor. (Note the imaging sensor here can be a camera or an array of photo
diodes of a position-sensitive device (e.g., a 2D PSD).
From figure 4.15c, simple geometry shows that

⋅
⋅
bu bf
x = ----------------------- ; z = ----------------------- (4.12)
fcot α – u fcot α – u