Henry Hexmoor

1
Fuzzy logic

• Henry Hexmoor
• Southern Illinois University
• Faner Hall, Room 2130
• Carbondale, IL 62901

2
Fuzzy Logic

• The value of a proposition John has a fever
  takes truth value in the interval 0-1.

1.0
0.0
95 96 97 98 99 100 101 102 103 014 105 106 107
Temperatures
3
Fuzzy Logic

• T(p and q) min (T(p), T(q))
• T(p or q) max (T(p), T(q))
• T(not p) 1 T(p)
• T(p ? q) min (1, 1 - T(p) T(q))

4
Fuzzy Logic

• Let's consider the following rules
• 1. obstacle very-close and left-side clear and
  right-side clear -gt move left
• 2. obstacle very-close and left-side tight and
  right-side tight -gt move tight-left
• 3. obstacle very-close and left-side tight and
  right-side clear -gt move right
• 4. obstacle very-close and left-side clear and
  right-side tight -gt move left
• 5. obstacle very-close and left-side closed and
  right-side tight -gt move tight-right
• 6. obstacle very-close and left-side tight and
  right-side closed -gt move tight-left

5
Fuzzy Logic

• Let's have the following functions

Very Close
Closed
Tight Left
1.0
1.0
1.0
0.0
0.0
0.0
-90 0 90
1 10
1 10
Dist to obstacle
Side Clearance
Direction change
Clear
Move Left
Tight Right
1.0
1.0
1.0
0.0
0.0
0.0
-90 0 90
-90 0 90
1 10
Side Clearance
Direction change
Direction change
Tight
Move Right
1.0
1.0
0.0
0.0
-90 0 90
1 10
Side Clearance
Direction change
6
Fuzzy Logic

• To apply the rules, we follow these steps
• 1. Get input. Suppose we get input of obstacle
  being 3 feet in front left side has a 1 foot
  clearance and right side has a 5 foot clearance.
• 2. Let's examine the applicability of left hand
  sides of the rules. AND in the left hand side
  means minimum. The resulting numbers are
  MODULATED values. I.e., the degree to which the
  rules will be activated.
• .8, .0, 1. gt 0.
• .8, .8, .5 gt .5
• .8, .8, .2 gt .2
• .8, .2, .8 gt .2
• .8, .8, .5 gt .5
• .8, .8. .8 gt .8
• 3. Scale down curves on the right hand side by
  the modulation factors.
• 4. Overlap and sum the scaled down function on
  the right hand side. Scale the summed curve to
  fit the range 0-1.
• 5. Find the place on the horizontal axis of
  output furntions that divides the space under the
  functions into two equal areas to the left and
  right. This is called finding the center of
  gravity for the output function. The value on the
  horizontal axis found is the ARBITRATED value
  sent to the actuators. In this case this will be
  amount of steering.

7
Fuzzy Logic

• 3. Scale down curves on the right hand side by
  the modulation factors.
• 4. Overlap and sum the scaled down function on
  the right hand side. Scale the summed curve to
  fit the range 0.0-1.0.
• 5. Find the place on the horizontal axis of
  output functions that divides the space under the
  functions into two equal areas to the left and
  right. This is called finding the center of
  gravity for the output function. The value on the
  horizontal axis found is the ARBITRATED value
  sent to the actuators. In this case this will be
  amount of steering.