Sistemi per il Governo dei Robot

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Sistemi per il Governo dei Robot

Silvia Rossi - Lezione 14

mercoledì 28 novembre 12

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ARCHITETTURE REATTIVE

FUZZY

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Behavioral Coordination: Fuzzy

Lofti Zadeh

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Maze Problem

Could use pfields Corridor following?

Wall following?

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Or...

3 behaviors, one for each sensor Combine with rules

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Maze Problem

If left sensor is too close and right sensor is too far then

turn right.

If left-sensor is just right and forward sensor is too far then drive straight.

If left-sensor is too far and

forward sensor is too far then turn left.

If forward sensor is close then turn right sharply.

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Maze Problem

If left sensor is too close and right sensor is too far then

turn right.

If left-sensor is just right and forward sensor is too far then drive straight.

If left-sensor is too far and

forward sensor is too far then turn left.

If forward sensor is close then turn right sharply.

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Not Regular “Production” Rules

If left sensor is too close and right sensor is too far then

turn right.

If left-sensor is just right and forward sensor is too far then drive straight.

If left-sensor is too far and

forward sensor is too far then turn left.

If forward sensor is close then turn right sharply.

Imprecise inputs and outputs (fuzzy)

ALL rules execute, not just the first one that is “true”

The “truth” of the output is an area under a curve

The “area” is like a proportional vote for an outcome

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Not Regular “Production” Rules

Imprecise inputs and outputs (fuzzy)

ALL rules execute, not just the first one that is “true”

The “truth” of the output is an area under a curve

The “area” is like a proportional vote for an outcome

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So How To Do This?

If left sensor is too close and right sensor is too far then

turn right.

If left-sensor is just right and forward sensor is too far then drive straight.

If left-sensor is too far and

forward sensor is too far then turn left.

If forward sensor is close then turn right sharply.

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General Procedure

1. Fuzzification: Perceptual Schema generates fuzzy inputs for the rules

Have a set of INPUT SETS that convert sensor reading to a fuzzi value or strength

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Fuzzification

Have pre-defined fuzzy sets which are like look up tables:

x-axis is the sensed reading

y-axis is the membership or strength in EACH set

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Fuzzification (up, left)

Reading: 320

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Fuzzification (up, left)

Reading: 320

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Fuzzification (up, left)

Reading: 320

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Fuzzification (up, left)

Reading: 320

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Membership Function

PROXIMITY Membership function for Sensor Left 320 is:

(Mc=0.66, Mr=0.33, Mf=0.00)

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Left-Sensor

Reading is 320, Fuzzification is (Mc=0.66, Mr=0.33, Mf=0.00)

If left sensor is too close (0.66) and right sensor is too far then turn right.

If left-sensor is just right (0.33) and forward sensor is too far then drive straight.

If left-sensor is too far (0.00) and forward sensor is too far then turn left.

If forward sensor is close then turn right sharply.

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Other Sensors (iterate)

Forward Sensor Membership function for 640 is:

(Mc=0.00, Mr=1.00, Mf=0.00)

Sensor-Rigt Membership function for 1024 is:

(Mc=0.00, Mr=0.00, Mf=1.00)

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Fuzzification is Complete

Left-sensor: (Mc=0.66, Mr=0.33, Mf=0.00)

Forward-sensor: (Mc=0.00, Mr=1.00, Mf=0.00) Right-sensor: (Mc=0.00, Mr=0.00, Mf=1.00)

If left sensor is too close (0.66) and right sensor is too far (1.00) then turn right.

If left-sensor is just right (0.33) and forward sensor is too far (0.33 for the ex.) then drive straight.

If left-sensor is too far (0.00) and forward sensor is too (0.00) far then turn left.

If forward sensor is close (0.00) then turn right sharply.

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Next Step

2. Apply fuzzy rules (Fuzzy Rules, by motor schema)

Get the strength of each rule which is called the fuzzy output The strength of the IF is the strength of the output

If left sensor is too close (0.66) and right sensor is too far (1.00) then turn right.

If left-sensor is just right (0.33) and forward sensor is too far (0.33 for the ex.) then drive straight.

If left-sensor is too far (0.00) and forward sensor is too (0.00) far then turn left.

If forward sensor is close (0.00) then turn right sharply.

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Evaluating Rules

If left sensor is too close (0.66) and right sensor is too far (1.00) then turn right.

If left-sensor is just right (0.33) and forward sensor is too far (0.33 for the ex.) then

drive straight.

If left-sensor is too far (0.00) and forward sensor is too (0.00) far then turn left.

If forward sensor is close (0.00) then turn right sharply.

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Boolean Operators

A AND B is minimum(A, B) A OR B is maximum(A, B) NOT A is 1-A

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Evaluating Rules

If left sensor is too close (0.66) and right sensor is too far (1.00) then turn right.

If left-sensor is just right (0.33) and forward sensor is too far (0.33 for the ex.) then

drive straight.

If left-sensor is too far (0.00) and forward sensor is too (0.00) far then turn left.

If forward sensor is close (0.00) then turn right sharply.

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Final Step

If left sensor is too close (0.66) and right sensor is too far (1.00) then turn right.

If left-sensor is just right (0.33) and forward sensor is too far (0.33 for the ex.) then

drive straight.

If left-sensor is too far (0.00) and forward sensor is too (0.00) far then turn left.

If forward sensor is close (0.00) then turn right sharply.

Combine fuzzy outputs (Defuzzification)

Each motor schema or behavior produces fuzzy output, but this has to be converted to a single number

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Defuzzification

As with fuzzification, defuzzification relies on a fuzzy set that was prevously determined

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Defuzzification (right, down)

“Opposite” of fuzzification

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Defuzzification (right, down)

“Opposite” of fuzzification

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Defuzzification (right, down)

“Opposite” of fuzzification

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Defuzzification (right, down)

“Opposite” of fuzzification

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Hedges

If left sensor is too close (0.66) and right sensor is too far (1.00) then turn right.

If left-sensor is just right (0.33) and forward sensor is too far (0.33 for the ex.) then

drive straight.

If left-sensor is too far (0.00) and forward sensor is too (0.00) far then turn left.

If forward sensor is close (0.00) then turn right sharply.

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Hedges

Hedges move the set over

If left sensor is too close (0.66) and right sensor is too far (1.00) then turn right.

If left-sensor is just right (0.33) and forward sensor is too far (0.33 for the ex.) then drive straight.

If left-sensor is too far (0.00)

and forward sensor is too (0.00) far then turn left.

If forward sensor is close (0.00) then turn right sharply.

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Defuzzification (right, down)

Result is an area of the fuzziness of the output Find the centroid

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Defuzzification: Take the Centroid of Blended Area

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Alternative: Centroid of Largest Area

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Weighted Means

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Recap

Perceptual schema == fuzzification

Input sets can be schema knowledge

Membership function for the fuzzy variable TURN

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Recap

Motor schema == fuzzy rules and defuzzification Output set can be schema knowledge

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Fuzzy Logic

Input sets and output sets may look similar

because we tend to use trapezoids and between 3 to 5 sets, but they are different!

Sets can have many shapes, can be learned, do not have to be symmetric

The membership function is usually 0 to 1 (normalized) for convenience

There’s a huge body of work - this is most simple level

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Be aware of Problems

Consider the output of an avoid ...

And where would the centroid be?

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Be aware of Problems

Consider the output of an avoid ...

And where would the centroid be?

Consider the Centroid of Largest Area (CLA)

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Example

The Robot1 is in a race agaist another robot2.

During the race, Robot1 wants to stay ahead of

robot2, but must not run into the wall that is at the end of the track.

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Example

The Robot1 is in a race agaist another robot2.

During the race, Robot1 wants to stay ahead of

robot2, but must not run into the wall that is at the end of the track.

The wall is 4 feet away.

The robot2 is 5 feet away

Robot1 is currently moving at 8 ft/s

Une Robot1 Fuzzy rules to determine how fast Robbie Shold go

The sets and rules are given a priori

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Robot1’s Rules

if the WALL is CLOSE and SPEED is FAST,

then SPEED is SLOW

If robot2 is NOT FAR,

then SPEED is FAST

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Mfast = 0.8

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Mclose = 0.5

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Robot1’s Rules

if WALL is CLOSE (Mclose = 0.5) and SPEED is FAST (Mfast = 0.8),

then SPEED is SLOW

If robot2 is NOT FAR (Mfar = 0.375),

then SPEED is FAST

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Robot1’s Rules

min(0.5, 0.8) Mslow = 0.5

NOT(1 - 0.375) Mfast = 0.625

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Defuzzification

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Defuzzification

5.62

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