The stair representation used for this development has been drawn relative to the
plane of motion of the Andros, as shown in Figure B-1. This reference frame is
appropriate as the sensor array moves along a path parallel to the plane of motion of the
Andros and the measured distances are relative to this plane, and not to the ground plane.
The single stair representation shown is defined by its rise, run, and the angle, P, which is
determined through basic geometry and is constructed of two lines that are perpendicular
to each other at their single point of intersection. As the stair representation is
constructed of two linear equations, one for the rise and one for the run, two separate
equations for the distance, d, must be developed. The distance, d, is the range distance
measured from the infrared sensor to the profile of the stair.
Y
(xo,yo) a (xy)
j-X
"__ _ x
Stair Runner
Figure B-2: Stair runner model
1