Page 177 - Designing Autonomous Mobile Robots : Inside the Mindo f an Intellegent Machine

Chapter 11

good (nearly unity). On the first set of ranges, the vehicle will take only a small cor-
rection. If, however, that correction was valid, and the next set of ranges is in general
agreement with the first, then the azimuth quality of this second calculation will be
slightly higher and the robot will take a more significant proportion of the implied
correction. If this trend continues for a few cycles, the robot will begin to aggres-
sively believe most of the corrections implied by the sensor. If the first correction
had been invalid, however, the robot would not have significantly degenerated its
position estimate.

If our robot can observe other columns or landmarks at the same time, then deciding
which set of columns to use can be as simple as comparing the fit qualities and
taking the best pair. A more exacting approach is to use fuzzy democracy and allow
all the implied corrections a vote proportional to their calculated qualities. For
example, if there are two reasonable implied corrections Φ and Φ with fit quali-
AB BC
ties Q FIT-AB and Q FIT-BC , then the correction could be calculated as:
Φ COR = ((Q FIT-AB AB FIT-BC BC FIT-AB + Q FIT-BC) (Equation 11.6)
*Φ ) + (Q
*Φ )) / (Q
Also note that the larger the spacing S between columns, the better the resolution
on heading will be for any given measurement noise in the implied centers of the
columns. A better representation of the image quality of a pair of columns might
consider this.
The nice thing about fuzzy navigation, however, is that it is not necessary to pre-
cisely quantify the quality factors; if they are reasonable, the system will converge on
the proper solution very quickly. If our system is converging too slowly, then most
likely our quality factors are too stringent. If it is over-correcting, then our quality
factors are probably too generous.

We have yet to correct the lateral and longitudinal axes. These implied corrections
will be equal to the apparent displacement of the features after compensating for the
azimuth displacement. We will use the closest feature (A), because the effect of any
error in the measured azimuth displacement will be smaller. To compensate for the
heading error, we find the vector from the center of our position estimate to the
measured center of the column A′. We simply rotate this vector by the implied
azimuth error, but in the opposite direction, and then add it back to our position
estimate and the result is the compensated position A″. The displacement of A″
from the programmed position A is our full implied position error, consisting of a
lateral and a longitudinal component. For simplicity, we will refer to lateral dimen-

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