Each infrared sensor constructs a digital representation of the staircase as the Andros

moves on it by determining the distance from the sensor to the staircase. By assuming

that the vehicle maintains a relatively constant velocity upon the staircase, the derivative

of the stair data can be found by simply taking the difference of the current data point and

the previous data point collected. The second derivative of the stair data can now be

obtained by taking the difference of the first derivative data. Figure 2-8 depicts a sample

stair data representation for a single infrared detector and the corresponding first and

second derivative data. The graph has been cropped to emphasize the range of pertinent

data. The data for the stair representation was simulated using a mathematical model of

the sensor system, with the first and second derivative data obtained as outlined above.

For the simulation, the rise of a single step was set at 8 inches, the run was set at 10

inches, and a 0.1 second sampling rate was used. Derivation of the mathematical model

of the sensor system can be found in Appendix B.


 Raw Data
 4 3 5 4 9 5 1 4




 3 3 4 4 1 1
 SortedData 4 4 5 5 5 4

 5 5 9 9 9 5



 Filtered Data
Figure 2-9: Median filter example