Probabilistic Smart Terrain

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Probabilistic Smart Terrain

• Dr. John R. Sullins
• Youngstown State University

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Outline

• What is Smart Terrain?
• Why do we need to add probabilities?
• Estimating expected distances to objects that
  meet character needs
• Plausibility benchmarks and experimental results
• Adding knowledge learned during exploration
• Hierarchical application to games

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Smart Terrain
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Smart Terrain

• Characters have needs
• Example hunger
• Objects in world meet needs
• Example refrigerator with food inside
• Characters move to objects that meet needs

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Smart Terrain

• Objects meets needs ? transmits signal
• Signal weakens with distance
• Signal moves around objects

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Smart Terrain

• Characters follow signal to objects
• Move in direction of increasing signal
• No need for complex navigation

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Outline

• What is Smart Terrain?
• Why do we need to add probabilities?
• Estimating expected distances to objects that
  meet character needs
• Plausibility benchmarks and experimental results
• Adding knowledge learned during exploration
• Hierarchical application to games

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Need for Probabilities

• Smart terrain can result in implausible actions
• Room character has never visited
• Contains empty refrigerator
• Does not transmit signal
• Character ignores it
• Not plausible behavior!

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Probabilistic Smart Terrain

• Objects broadcast signal of formI meet need n
• I may meet need n with probability P
• Probability uncertainty that
  object meets need
• Character explore uncertain objects along path

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Probabilistic Smart Terrain

• Character should Move to closest object
  with highest probability
• Problem Optimizing two separate criteria
• Realistic Goal Plausible behavior

Meets hunger need with P 0.6 At distance 6
Meets hunger need with P 0.7 At distance 8
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Outline

• What is Smart Terrain?
• Why do we need to add probabilities?
• Estimating expected distances to objects that
  meet character needs
• Plausibility benchmarks and experimental results
• Adding knowledge learned during exploration
• Hierarchical application to games

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Expected Distances

• Expected number of tiles character must travel
• From current tile
• To object that fulfills need
• Based on
• di distances to each object i
• pi probabilities each object i meets need

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Expected Distances

• P(t) probability no objects within t tiles meet
  need
• 
  P(t) ? (1 pi ) (Equation
  1)
• where di lt
  t
• Based on assumption of conditional independence

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Expected Distances
Distance 6 Prob 0.6
Distance 8Prob 0.7

• t lt 6 P(t) 1
• 6 t lt 8 P(t) (1 0.6) 0.4
• t 8 P(t) (1 0.6)(1 0.7) 0.12

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Expected Distances

• Expected distance from tile T
  to tile that meets need
  E(T) S P(t) (Equation 2)
  t

t lt 6 P(t) 1
6 t lt 8 P(t) 0.4
t 8 P(t) 0.12
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Expected Distances

• Problem Sum could be infinite
• Solution Limit t to some tmax
  tmax gt di ?i
• tmax
• E(T) S P(t) (Equation
  3) t

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Expected Distances

• Compute expected distance E(T) for all tiles T
• Character moves to adjacent tile with lowest E(T)

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Outline

• What is Smart Terrain?
• Why do we need to add probabilities?
• Estimating expected distances to objects that
  meet character needs
• Plausibility benchmarks and experimental results
• Adding knowledge learned during exploration
• Hierarchical application to games

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Plausibility Benchmarks

• Goal for gamesNon-player characters should
  behave plausibly
• Move in direction that makes sense to player
• Benchmarks for plausible behavior
• Objects similar in either distance or probability
  
• Group of objects in same direction
• Objects that meet need with complete certainty

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Plausibility Benchmarks

• Objects at same distance ? move to higher
  probability
• Objects with same probability ? move to closer one

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Plausibility Benchmarks

• Nearly same distance ? move to much higher
  probability
• Nearly same probability ? move to much closer
  object

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Plausibility Benchmarks

• Aggregate probabilities benchmark
• Multiple objects gt single object with higher
  probability
• Assumption of conditional independence

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Plausibility Benchmarks

• Complete Certainty benchmark
• Single object with probability 1 gt
  multiple objects with probability
  lt 1

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Outline

• What is Smart Terrain?
• Why do we need to add probabilities?
• Estimating expected distances to objects that
  meet character needs
• Plausibility benchmarks and experimental results
• Adding knowledge learned during exploration
• Hierarchical application to games

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Learned Knowledge

• Probabilities changed when object reached
• Object meets need ? probability becomes 1
• Does not meet need ? probability becomes 0
• Should affect future actions

Refrigerator empty
Move towards another goal
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Learned Knowledge

• Changing global map affects all characters
• Will also appear to have learned this knowledge

New character enters room
Also ignores empty refrigerator
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Learned Knowledge

• Each character stores own world model
• Belief object meets needs
• Initially based on probabilities
• Modified when objects explored

0
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Learned Knowledge

• Each object propagates raw data to tiles
• Probability it meets need
• Distance to that tile

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Learned Knowledge

• Character examines surrounding tiles
• Modify probabilities using world model
• Compute expected distances for each

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Outline

• What is Smart Terrain?
• Why do we need to add probabilities?
• Estimating expected distances to objects that
  meet character needs
• Plausibility benchmarks and experimental results
• Adding knowledge learned during exploration
• Hierarchical application to games

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Hierarchical Smart Terrain

• More realistic scenario
• Know whether objects meet needs
• Dont know if object is present in given area

• Go to entrance of most likely area

• If object not present, move to another area

• If object present, move to it

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Hierarchical Smart Terrain

• Area attractors at entrances to rooms
• Broadcast to entire level
• Probability object that meets need is in room
• Probability set to 0 when reached by character
• Objects in room
• Signal range size of room
• Probability 1 if present in room

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Hierarchical Smart Terrain

• Compute expected distances from area attractors
• Move to best room

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Hierarchical Smart Terrain

• Object is present in area
• Now in range of object, probability meets need
  1
• Character will move directly to object

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Hierarchical Smart Terrain

• Object is not present in area
• Set probability of area attractor 0
• Character will move to next plausible attractor

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Conclusions

• Probabilities added to Smart Terrain algorithm
• Characters move to adjacent tile with shortest
  expected distance to a tile that meets need
• Algorithm produces plausible behavior for
  benchmarks
• Probabilities overridden by learned knowledge
• Hierarchical algorithm for realistic play

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Ongoing Work

• Characters with multiple needs at different
  levels
• Low-probability object that meets critical need
• High-probability object that meets less critical
  need
• Which to move towards?
• Objects that change over time
• Empty refrigerator now may be restocked in future
• Searching for other characters who move from
  place to place