using quantum fuzzy logic to learn facial gestures of a schrödinger cat puppet for robot theater...

Using Quantum Fuzzy Logic to learn facial gestures of a Schrödinger Cat puppet for

Robot Theater

Arushi RaghuvanshiProf. Marek Perkowski

24 May 20081

Background: Quantum Robots

H

A B

P QL1 L2

S1 S2

M1

M2

M3 M4

M5 M6

Quantum Braitenberg

Mr PotatoHead

Old Duck Biped

Schrödinger's Cat

*character in Interactive Robot Theatre2

(ISMVL 2007)

Programming Robot Behaviors

BehaviorSelection

Theatre Director

Input Initialization

Quantum or other logic controller

Measurement Effectors

sound

Simple sequential flow with no feedback

3


BehaviorSelection

Theatre Director




sound

Adding emotions and environmental feedback

emotionEnvironment

including human audience

Theatre Director

4


BehaviorSelection

Theatre Director




sound

Emotional Interactive Robots with Sensors and Feedback Modifying the Behavior

emotionEnvironment

including human audience

Theatre Director sensors

5

Quantum & Fuzzy LogicQuantum Circuit

(Can be transformed into Quantum Fuzzy Logic, by replacing gates)

NOT -> Fuzzy NOTOR -> MAXAND -> MIN

Fuzzy Logic with MIN & MAX operators

New Operators and Literals can be defined for Quantum Fuzzy Logic

6

Fuzzy Logic Example

7

0.3

0.7

0.3

0.70.7

0.30.3

0.7

0.3

0.7

0

0.3

1

0.7

0.7

0.3

Fuzzy Logic Operations

8

• Multiple ways to create Fuzzy operations• Two examples below• Example 1

– NOT (a) = (1 – a) • e.g. NOT (0.34) = 0.66

– MIN (a, b) = if (a < b) then a else b • e.g. MIN (0.3, 0.75) = 0.3

– MAX (a, b) = if (a > b) then a else b• e.g. MAX (0.63, 0.83) = 0.83

• Example 2– NOT (a) = (1 – a)

• e.g. NOT (0.34) = 0.66

– MIN (a, b) = a * b• e.g. MIN (0.3, 0.7) = 0.21

– MAX (a, b) = (a + b) – a*b• e.g. MAX (0.3, 0.7) = 0.3+0.7-0.21 = 0.79

• As in example 2, MAX and MIN may be misnomers. They can be called OR and AND operations instead

a MAX b = NOT ( NOT (a) MIN NOT (b))

=NOT ((1-a)*(1-b))

=NOT(1-a-b+a*b)

=1-1+a+b-a*b

=a+b-a*b

Z

YX

0

1

1

-1

-1

1

-1

|0›

|1›

Representing Fuzzy Values on Bloch Sphere

• Fuzzy values can be represented in different ways on Bloch Sphere

• Simplest way to represent is along the meridian (as shown on left)

• After measurement, value can be 0, 1 or anywhere in between

• Other mechanisms (e.g. values inside the Bloch Sphere, or parallels of latitudes etc. ) can also be used

9Measurements

00.15

0.5

0.81

Quantum Fuzzy Literals

Rotation Around Y Axis Rotation Around X Axis Phase Shift (270 degree rotation around Z axis)

We use this to define the Fuzzy NOT operations (Other literals can be used as well).

10

X

Z

Y

Quantum Fuzzy ‘NOT’ operator

Inverter is defined in exactly the same way as in quantum logic:

Fuzzy Quantum Not(α|0 +β|1)β|0 +α |1

where the square of the (in general complex) value associated with ket |1 is an equivalent of fuzzy value in interval [0, 1].

11

1 0 0 0 0 0 0 00 1 0 0 0 0 0 00 0 1 0 0 0 0 00 0 0 1 0 0 0 00 0 0 0 1 0 0 00 0 0 0 0 1 0 00 0 0 0 0 0 0 10 0 0 0 0 0 1 0

0 R (Davio)

α1|0 + α2|1

β1|0 + β2|1α1β1|000 + α1β2|010 + α2β1|100 + α2β2|111

= (α1β1|00 + α1β2|01 + α2β1|10) |0 + (α2β2|11) |1

=> Probability of measurement

of ‘1’ is |α2β2 2

α1β10 α1β20α2β100α2β2

000

001

010

011

100

101

110

111

α1β1α1β2α2β1α2β2

α1α2

β1β2

10

Input is Kroenekar product of 3 parallel input lines

=10

=



=X

Toffoli Gate

Input Matrix Output Matrix

Quantum Fuzzy ‘MIN’ operatorMin (α1|0 + α2|1, β1|0 + β2|1 ) = Davio (α1|0 + α2|1, β1|0 + β2|1, 0)

Quantum Fuzzy ‘MAX’ operator

The definition of Fuzzy Quantum Maximum Operator is calculated from De Morgan rule:

A max B = NOT ( NOT (A) min NOT (B)).

13

Quantum Fuzzy Logic in Robots

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Fuzzy Value Sensors

Light Sensors 0 = completely dark0.5 = semi-dark 1 = completely bright

Sound Sensors0 = pin-drop silence0.5 = normal noise (people talking)1 = loud crash

Image Sensors Quantum Fuzzy Logic

Motor Controls causing output behaviors

Back to Robot Theatre….

Combination of Genetic Algorithm and Quantum Fuzzy Logic

15

Synchronizing Lips with Speech

Not This

Want This

16

Traditional Methods

• Use mapping of phonetic symbol to a lip shape (as shown on left)

• Sound streams can be parsed to generate phonetic symbols

• The methods are language dependent (i.e. different mapping for different language)

• Need to be modified for speed and style of speaking

17

Using Genetic AlgorithmsSound Input

Initial Set of genomes representing lip movements(initial population for GA)

These are dynamically generated by program

A

Input to Fitness Function(User evaluation – interactive)

ESRA Robot

Shows Lips Movements

B

*** The matching function is dynamic, so it doesn’t matter if people have different accents, talk slower/faster, etc.

GA Engine

Sequence representing Lip movements matching with input stream ‘A’

18

Genome

• A Genome (or a chromosome) is a pattern that corresponds to a behavior.

• A possible solution to the given problem can be encoded encoded to create a genome.

• In genetic algorithms, a set of random genomes are created.

• When decoded these genomes represent possible solutions to the given problem.

• In my experiment, a genome is an encoded string that represents a sequence of lip movements. For example:

49__9__31__9__46_1640__• When decoded, this code represents the lip motion for

the phrase “Hi I am a robot.”

19

Encoding Lip Shapes for Defining the Genome

Code 0, 1Upper: 127Lower: 127

Code 2Upper: 87Lower: 173





Code 7, 8Upper: 80Lower: 45

Code 9Upper: 100Lower: 45 20

Fitness Function

• The better the robot completes the problem, the higher the fitness function.

• When synchronizing sound and lip motion the fitness function would be a user input.

• To test the Genetic Algorithm, I calculated the fitness function by comparing the genomes to the best solution.

• The best solution was determined by the traditional method.

21

Fitness Function Algorithm

1 4 9 5 7 _ 3 8

5 3 _ 8 3 _ 3 8

↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑4 1 9 3 4 0 0 0

Best Genome (for calculating Fitness Score)

Genome Under Test

Find Difference for each corresponding element

• Closeness implies better match (4-3 is better than 1-5)

• Pauses ‘_’ must match in position to get any score, so it is either 0 or 9

9-X = 5 8 0 6 5 9 9 9

X =

Total Score = 5+8+0+6+5+9+9+9 = 51

Fitness Score % = (Total/TotalPossible)*100

= 51/72 * 100 = 70.83%

Higher number is better now !

22

Selection• The higher the fitness

score, the higher the probability of being selected.

• Selection methods include the Roulette Wheel, Tournament Selector, and Truncation Selection

• In my experiment, I used a Roulette Wheel for selection.

23

Crossover

When two chromosomes from the group are selected they are combined to create a new genome.

Dependent on the crossover rate the bits from each chosen genome are crossed at a randomly chosen point.

The higher the crossover rate is, the more likely it is that a crossover will occur.

The crossover occurs at a randomly chosen point in the genome.

24

Mutation• Depending on the

mutation rate, chosen bits of the genome are changed.

• The higher the mutation rate, the more likely it is that a bit will be changed.

• Shown to the right are many types of mutation

25

Mutation

• In my experiment I used two different mutation functions– Swap mutation– myMutator

• I created my own mutator which changes a single bit, rather than swapping two bits.

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Terminating ConditionsThis generational process is repeated until a termination

condition has been reached. Common terminating conditions are

* A solution is found that satisfies minimum criteria * Fixed number of generations reached * Allocated budget (computation time/money) reached * The highest ranking solution's fitness is reaching or has

reached a plateau such that successive iterations no longer produce better results

* Manual inspection * Combinations of the above.

I used a fixed number of generations as the ending criteria. Default-4,000 generations; I also experimented with changing the number of generations.

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initialize population

select individuals for mating based on Fitness Function

mate individuals to produce offspring

mutate offspring

insert offspring into population

are stopping criteria satisfied?

finish

Basic Genetic Algorithm Flow

28

GA for Lip Synchronization

Initial Set of genomes representing lip movements(initial population for GA)

These are dynamically generated by program

A

Interactive Input to Fitness Function

ESRA Robot


B

In real application, input to Fitness Function is dynamic, language independent, and it doesn’t matter if people have different accents, talk slower/faster, etc.

GA Engine

Sequence representing Lip movements matching with input stream ‘A’

Test Sound Input Matching Sequence for Automating

Fitness Fn Evaluationlength

original sound input

Automated Mode

Interactive Mode

29

Genetic Algorithm BehaviorsInput length vs Objective Score (Swap

mutator)

0.000

20.000

40.000

60.000

80.000

100.000

120.000

1 2 4 8 16 32 64 128

Input length (number of characters)

Input Length vs. Time (Swap Mutator)

0.000

1.000

2.000

3.000

4.000

5.000

6.000

7.000

8.000

9.000

10.000

1 2 4 8 16 32 64 128

Input Lenght(number of characters)

Input Length vs. Time (My Mutator)

0.000

2.000

4.000

6.000

8.000

10.000

12.000

14.000

1 2 4 8 16 32 64 128

Input Length (number of characters)

Avera

ge t

ime (

sec.m

illisec)

Input Length vs. Objective Score (My Mutator)

92.000

93.000

94.000

95.000

96.000

97.000

98.000

99.000

100.000

101.000

1 2 4 8 16 32 64 128

Input Length (number of characters)

Mutation Rate-Swap Mutator

70.000

75.000

80.000

85.000

90.000

95.000

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Mutation Rate (0-1)

Obj

ectiv

e S

core

(%)

Mutation Rate (My Mutator)

0

20

40

60

80

100

120

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Mutation Rate (from 0-1)

Obj

ectiv

e S

core

(%)

Crossover Rate vs. Objective Score

74.00076.00078.00080.00082.00084.00086.00088.00090.000

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Crossover Rate (0-1)

Obj

ectiv

e Sc

ore

(%)

Number of Generations vs. Objective Score

0.000

20.000

40.000

60.000

80.000

100.000

Number of Generations

Ob

jecti

ve S

co

re(%

)

Number of Generations vs. Avg Time

0.000

1.000

2.000

3.000

4.000

5.000

6.000

Number of Generations

Avg

. T

ime (

sec.m

illisec)

Population Size vs. Avg. Time

0.000

5.000

10.000

15.000

20.000

25.000

30.000

35.000

40.000

1 16 32 64 128 256 512

Population Size

Avg

. T

ime (

sec.m

illisec)

Population Size vs. Objective Score

80.000

82.000

84.000

86.000

88.000

90.000

92.000

94.000

1 16 32 64 128 256 512

Population Size

Number of Offspring vs. Avg. Time

1.240

1.260

1.280

1.300

1.320

1.340

1.360

1.380

1.400

1.420

1.440

1 2 4 8 16 32 64 128

Number of Off spring

Number of Offspring vs. Objective Score

78.00079.00080.00081.00082.00083.00084.00085.00086.00087.00088.00089.000

1 2 4 8 16 32 64 128

Number of Off spring

GA Results thus far..

• Created a self-learning robot that can learn how to synchronize sounds and words with appropriate facial expressions.

• Finding the best solution depends on different conditions. In general, I noticed that the functions that gave the higher objective scores tended to take more time to complete 4,000 generations.

34

Ongoing work• Combining Quantum Fuzzy Logic to Robotic

Theatre. • Modify the body language (hand and arm

movements) based on environmental sensors– Sound Sensors (fuzzy value input) to detect noisy or

quiet environments and modify behavior– Light sensor values (fuzzy value input) to detect day

and nights and modify behavior

• Quantum Fuzzy Schrödinger Cat sitting on Quantum Fuzzy Braitenberg vehicle arguing with Einstein, singing a song and going crazy .

35

Cat Singing

A lively little quantum went darting through the air, Just as happy quanta go speeding everywhere ………..

Thank You

37

Genetic Algorithms

A genetic algorithm is a search technique used in computing to find exact or approximate solutions to optimization and search problems. Genetic algorithms are a particular class of evolutionary algorithms that use techniques such as inheritance, mutation, selection, and crossover.

38

Traditional Method(Without Genetic Algorithms)

AudioSpeech

Recognition

PhoneticLetters,

Punctuation,and syllables

Matches inputto correctlip motion:

Static*** Since the matching function is static, it will have to be entirely recoded for different people: they have different accents, talk slower/faster, etc.

Sequence representing Lip movements matching with audio input string.

ESRA Robot


Language Dependent

39

ESRA Robot Facial Expressions

Motor for Eye Lids

Motor for Lower Lip

Motor for Upper Lip

• ESRA Robot has several motors for lips, eyelids and arm movements

• I am primarily using lip motors for my experiment

• Specific position of lip motors define the shape of the lip

• The shape can be matched with speech

40

Crossover

• Single Point Crossover• Double Point Crossover

gives any two points on each genome an equal chance of being split up.

• In my experiment, I used a single point crossover with a 90 percent crossover rate.

41

Procedure1. Create a robot with a face, a mouth, and two motors for lip movement.2. Assign shapes of the mouth for every sound/syllable3. Encode these shapes using numbers and characters4. Create a random set of genomes for a given input.5. Depending on the number of encodings that match with the appropriate

sound, a fitness function will be assigned to each genome.6. Using a Roulette Wheel, genomes will be selected for reproduction. The

higher the fitness score: the higher the probability of being selected for reproduction.

7. To create a new set of offspring, one random crossover point will be chosen for each pair of genomes.

8. There will also be a 1% mutation rate.9. A new set of genomes (the offspring) are created.10. Repeat steps 5-9 for a fixed number of generations.11. Change the Genetic Algorithm parameters and record the dependent

variables.

42

Program

• I used GALib from MIT lab as a library in my program.

• I designed my own genome• Defined my fitness function• Created an initializer function• Created a mutator function• Program link- Project file• EsraGA- Main C++ source code

43

Data

Data Tables with swap mutator

Data Tables with my mutator

44

AbstractThe purpose of this project is to create efficient Genetic Algorithms

for robotic learning and the synchronization of speech and visual expressions. This experiment uses an ESRA robot which has a set of motors to control facial expressions including lip motion and eyebrow motion. Emotions can be created using facial expressions and arm motion; however, for the simplicity of this experiment, the focus is on lip motion. Various shapes of the mouth are assigned to the appropriate sounds and encoded. Using these encodings I create a random set of chromosomes. I then use Genetic Algorithms so the robot can develop the lip motion to correspond with spoken text. Next, I use the Genetic Algorithm to test how long it takes to synchronize text and lip motion for varying length, crossover rate, mutation rate, number of generations, population size, and number of offspring. Overall, I concluded that my hypothesis was supported because using genetic algorithms for behavioral evolution, I was able to create a robot that can learn how to synchronize sounds and words with appropriate facial expressions. After testing various parameters, I concluded that functions that return higher objective scores, take a longer time to complete. Some applications of this project include translating text into lip motion for animation movies and humanoid robots. The next step in this project would be to try different parameters such as convergence and migrating populations. I could also develop body language as well as lip motion. 45

Applications• With a program using genetic algorithms, matching lip

movements to speech are language independent. Also, one can use the same program for different people. In the traditional style, the tables would have to be recoded because everyone has individual accents, body language, and how fast they talk.

• This program can be used to match text and lip motion for movie animation and humanoid robots.

• Animation industries don’t have to hand draw lip motion or use a databank of words. This would be most affective if I used a combination of pre-programmed lipcodes and user inputs.

• This could be used to convert sounds into lip motion so deaf people can understand what is being said in situations in which they can’t see the person who is speaking. I

• t could also be used in reverse and convert lip motion into text. This could be useful in documenting presentations, speeches, and even court cases. It could also be used to create subtitles in movies.

46

Representing Fuzzy Values on Bloch Sphere

• Show L1 through L5 options

47

Synchronizing Lips with Speech

Not This

Want This

48

using quantum fuzzy logic to learn facial gestures of a schrödinger cat puppet for robot theater...

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