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Transcript
```Let’s play snooker
Group 2
Yannick Thimister
Frans van den Heuvel
Enno Ruijters
Esther Verhoef
Ali B. Ozmen
Achim Leydecker
1
Overview







Physics and noise – Ali
Simple method – Frans
Complex method - Enno
Product demonstration - Esther
Experiments and results - Achim
Conclusion - Yannick
2
Design and implement an artificial
intelligence for a Snooker simulation
with a realistic physics model,
including noise. Then determine the
effects of this noise on the artificial
intelligence.
3
Physics
• Spin & Cue Ball
• Impulse
• Noise Model
4
Spin and Cue ball
 ...........0........... 


V    Fx cos  / M CB 
 ...........0........... 


  FZ  sin   Fy  cos  

 2

   FZ  sin 
   5 M CB R 

  F  cos 
 
x


V: Linear velocity
ω: Angular velocity
F: Force acting on ball by cue
F: Force acting on ball by cue
M: Mass of cue ball
M: Mass of cue ball
θ: Angle between q and x-y plane
θ: Angle between q and x-y plane
R : Radius of the cue ball
J=
Impulse
• Collisions between balls are handled by adding a
certain amount of impulsive force to both balls in
opposite directions.
• The magnitude of this impulse is given by the
equation ;
Impulse
• When we used to calculate the change in velocity in
the collision, previous equation can be simplified into
this equation:
• By assuming the two balls have the same mass,
since the masses are factored out again when
converting the change in momentum into the
corresponding change in velocity.
Noise Model
A set of standard deviations
• Five parameters specified
(4 Input parameter & Coefficient of friction )
• Error is modeled by perturbing these 5 parameters
by zero – means Gaussian noise.
Simple method
• Repeated random sampling
• All directions / variation of force / No
spin
• Two versions
• Iterate through the 50 best shots
• Highest average amount of points
• Easy implementation & good results
Tactical method
•
•
•
Extended version of Simple AI
–
–
•
Avoid complex shots
Use tactics to improve future shots
Naturally more resistant to noise
10
Tactical method(complexity
avoidance)
•
Minimize number of collisions
–
–
•
Ignore irrelevant collisions
Collisions between two moving
balls strongly avoided
Minimize distance traveled
–
Again, ignore irrelevant paths
11
Tactical method (snooker tactic)
•


Snooker if no potting possible
Avoid snookering yourself
Considers only direct snookers
12
Tactical method(easy ball tactic)
•


Try to leave easy balls for later
shots
Avoid impossible shots later
Problem: helping opponent?
13
Tactical method(shot evaluation)
•
•
•
•
•
Initial score based on actual points
gained
Scale by penalty for every collision
– Exponential reduction
Scale linearly by distance
14
Program demonstration
15
Experiments

Basic setup




100 full games per experiment
No player change
Foul points are subtracted from the
total points
Average and standard deviation are
recorded
Experiments

Noise


All four types of noise are tested
separately with five different degrees
of intensity
Fixed maximum number of random
samples
Experiments
Experiments

Number of random samples


Fixed noise level (2)
Effects of heuristics for tactical
method




Fixed noise level (2)
Each tactic is tested separately
Collision-avoidance & distanceminimization only
Snookering is tested by playing
against the simple method with 500
random samples
Results
Tactical vs. simple
Total points Tactical
Total Points simple
144.3
144.2
127.4
124.8
106.4
95.8
87.6
95
87
71.6
88.8
69.8
69.8
53.4
53
37.9
27
10.6
No noise
N0
Only noise Only noise Only noise Only noise All noise,
in force of in contact
in cue
in table
level N1
shot
point
angle
friction
All noise,
level N2
All noise,
level N3
All noise,
level
N_{4}
Results
Conclusion
• Both methods decrease in