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