Page 67 - Designing Autonomous Mobile Robots : Inside the Mindo f an Intellegent Machine

Chapter 4

Trapezoidal fuzzy logic is nothing more than a way of defining the contribution of
inputs to an output using only straight line functions. Each point is either an end
point, or it is the intersection of two adjoining line segments.

Let’s assume that we have digitized the outputs of the detector / amplifiers of Figure
4.2 and scaled them as 0–100%. To combine these signals into a single “threat
score,” we have only to define a series of line segments that monotonically express the
relationship as shown in Figure 4.3. By monotonic, we simply mean that for any value
of signal strength there is one and only one value of threat contribution, or in other
words the curves don’t double back over themselves.

In this case, the PIR signal transfer function is defined by P0, P1, P2, and P3, where-
as the MW signal transfer function has only P0, P1, and P2 as distinct points. For
purposes of calculation, the third point (P3) can be simply defined as having the
same value as P2. Notice that there is no absolute rule for the number of points, and
if need be the functions can have many more line segments.
In the case of our motion detector, we have decided that we don’t want the PIR to
contribute to the threat score if it is indicating less than 20% of full scale, because
signals below this range are commonly experienced as background noise. This is re-
ferred to as its dead band, and is the range between P0 and P1. The MW sensor is
even noisier, so we have given it a dead band of 30%. The dead band assures that we
cannot produce an alarm state with one sensor in a region so low that it only repre-
sents normal background noise.

The highest threat contribution we have allowed for PIR is 80 units, and the highest
for MW is 60 units. Thus, if we set the alarm threshold to 75 units, the PIR alone
could cause an alarm if it approached 100% of full-scale input, but the MW could
not produce an alarm by itself. However, if we set the threshold above 80 units,
neither sensor by itself could cause an alarm, and thus both would need to be above
their P1 points.
Consider the case where the two sensors are responding at the levels indicated by
the stars. The PIR is contributing about 58 units of threat, while the MW is contrib-
uting 75 units. Thus, the threat score is 58 + 75 or 133 units. If this is greater than
our alarm threshold, we have an alarm condition.

Fuzzy democracy

Perhaps the most frustrating quality of democracy is that everyone gets one vote,
whether they understand the issues at stake or not. A person with a great deal of

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