Page 176 - Designing Autonomous Mobile Robots : Inside the Mindo f an Intellegent Machine

Hard Navigation vs. Fuzzy Navigation

the columns varied only 40% of the radius, as shown by the shaded circles in
Figure 11.9, then the variation this would imply for the heading correction could
range from –Φ1 to –Φ2. Notice that the –Φ1 correction is nearly twice the calcu-
lated –Φ in Figure 11.8, while the –Φ2 correction is nearly zero.

Both Φ1 and Φ2 are in the same direction, so there is likely to be some truth in
their implications, we just don’t know how seriously to take them. We can apply
other checks as gatekeepers before we must decide how much of the correction –Φ
we want to apply to our odometry. We have already calculated the image quality of each
column, and rejected the use of any columns that were not above a reasonable
threshold. We can also check the distance between the implied centers of the col-
umns and make sure it is close to the programmed spacing (S).
Now the time has come to decide the quality of the heading correction implied by
these ranges. To do this we calculate the heading correction believability or azimuth
quality of the implied correction. The azimuth correction quality is:
Q = (U – |Φ|) / U AZ (Equation 11.3)
AZ
AZ
Here U is the current azimuth (heading) uncertainty. Note that as the implied cor-
AZ
rection becomes small with respect to the heading uncertainty, the quality approaches
unity. If the implied correction is equal to or greater than the azimuth uncertainty,
the quality is taken as zero.

Again, there are two reasons we might not believe this whole heading correction:
first, because the data that created it was not clean (or there was not enough of it to
know if it was clean); and secondly, because the correction did not seem reasonable
given the robot’s confidence in its current heading estimate. Therefore, we can
reduce the amount of an implied correction by simply multiplying it by the various
quality factors that affect it. If Q is the image quality for column A and Q is the
A
B
image quality for column B, then fit quality for the whole implied azimuth correction
is:
Q = Q * Q * Q (Equation 11.4)
FIT A B AZ
The correction Φ COR to be used on this cycle will be:

Φ COR = – (Q * Φ) (Equation 11.5)
FIT
To understand how simply this works, consider a robot imaging these columns and
returning a low azimuth quality because the implied correction is nearly as large as
its azimuth uncertainty. For argument’s sake, let’s say that the image quality is very

159