Page 316 - Concise Encyclopedia of Robotics

Stadimetry
similar to the azimuth bearing used by astronomers and navigators,
except that it is measured counterclockwise rather than clockwise. As a
ray rotates around a full circle through all possible values of x, it defines
a reference plane.
The second angle, call it y, is measured either upward or downward
from the reference plane. The value of y will ideally range from 90°
(straight down) to +90° (straight up). Structural limitations of the robot
arm might limit the lower end of this range to something like 70°. You
might think of y as the elevation above or below the horizon.
The radius, denoted r, is a non-negative real number (zero or greater).
It can be specified in units such as centimeters, millimeters, or inches.
The illustration shows a robot arm equipped for spherical coordinate
geometry. The movements x, y, and r are called base rotation, elevation, and
reach, respectively. Compare CARTESIAN COORDINATE GEOMETRY, CYLINDRICAL COORDINATE
GEOMETRY, POLAR COORDINATE GEOMETRY, and REVOLUTE GEOMETRY.
STADIMETRY
Stadimetry is a method that a robot can use to measure the distance to an
object when the object’s height, width, or diameter is known. The vision
system and controller ascertain the angular diameter of the object. The
linear dimension of the object must be known. The distance can then be
calculated using trigonometry.
Camera θ
d h

Stadimetry
The illustration shows an example of stadimetry as it might be used
to measure the distance d, in meters, from a robot camera to a person.
Suppose the person’s height h, in meters, is known. The vision system
determines the angle
that the person subtends in the field of view.
From this information, the distance d is calculated according to the
following formula:

h
d =
2 tan(
/2)
If the distance d is large compared with the height h, a simpler formula
can be used:

