Multiagent Probabilistic Smart Terrain Dr. John R. Sullins Youngstown State University.

Multiagent Probabilistic Smart Terrain

Dr. John R. Sullins

Youngstown State University

John Sullins Youngstown State University

Multiagent Probabilistic Smart Terrain CGAMES 2011

2

Multi-Agent Search in Games

• Player in someroom on thislevel

• Multiple guardssearching forplayer

• Some roomsmore likelythan others



3

Multi-Agent Search in Games

• Guards must“divide up” rooms inplausible way

• Focus on most likely rooms

• While makingsure all roomssearched



4

Outline

• Goals of multi-agent probabilistic search

• Background: Probabilistic smart terrain

• Estimating global expected distances to targets that meet goals of group

• Matching agents to targets

• Demonstration on examples



5

Multi-Agent Smart Terrain

• Assumptions: – “Teams” of NPCs with same goal (such as “find player”)– One NPC finds target that meets goal

entire team succeeds

• Must be fast solution – No time for complex negotiations among characters– Plausible behavior from POV of player sufficient



6

Plausibility Benchmarks

• Cooperative behavior:– Room 1 closer to G1 and more probable than room 2– G1 should still move to room 2– G2 can cover room 1– Both rooms searched quickly



7


• Probability as a factor:– Room 1 much more probable than room 2– G1 should move directly to room 1– Player overwhelmingly likely to be found there

• Main purpose: Find goal, not search all targets



8


• Divide and conquer:– G1 closer to both rooms and could explore both– G2 should still move to the rooms also even though closer to

neither– If G1 moves to one room, G2 can quickly cover the other



9

Outline








10

Smart Terrain

• Target meets goals transmits “signal”– Signal moves around objects, weakens with distance

• Character follows signal to target



11

Limits of Smart Terrain

• Normal smart terrain not appropriate for all situations

• “Guard search” example:– Player “transmits signal”– Guards follow directly to player– Obvious cheat!

• Guards should have to search for player based on probabilities



12

Probabilistic Smart Terrain

• Targets broadcast signal of form “I meet goal”

“I may meet goal with probability P ”



13

Expected Distances

• Expected number of tiles character must travel from tile x to target that meets goal

dmax

Dist(x) = Σ (1 – pi ) d=0 di < d

Probability no target within d tiles of x meets goal

(assumption of conditional independence)

Summed over all distancesup to some maximum dmax

(otherwise sum could be infinite)

• Compute Dist(x) for adjacent tiles x• Move to adjacent tile with lowest Dist(x)



CGAMES 2011

14

Expected Distances

p = 0.6

distance = 8

p = 0.7

distance = 6



15

Outline








16

Global Expected Distances

• Each agent Aj estimates moves until goal found by some agent (not necessarily itself)

– Distances to targets Aj is moving towards

– Distances of other agents to targets Aj is moving away from



17

Finding Closest Targets

• Step 1: Each agent Aj determines set of targets Tj that it is closer to than any other agent



18

Partitioning by Direction

• Step 2: For each possible next tile for Aj, determine which targets Tj direction Tj would be closer in that direction

• Tj left

• Tj right

• Tj up

• Tj down



19


• Step 3: Compute global expected distance for each possible next tile x based on targets ti Tj

dmax

Dist(x) = Σ (1 – pi ) d=0 di < d

• ti Tj direction di = distance(x, ti ) + 1

• ti Tj direction di = min(distance(Ak, ti ))

j ≠ k

(distance to closest other uncommitted agent)



20


• Tj left

• Tj right

• Tj up

• Tj down



21


• Example: Expected global distance for A1 moving left– Neither room reached in < 4 moves

– A1 reaches room 2 (probability 0.4) in 4 moves

– A2 reaches room 1 (probability 0.5) in 5 moves

• Each agent computes global expected distances for surrounding tiles

• Each agent then moves to tile with the lowest global expected distance



22

Moving Agents

A1 moves rightA1 moves left



23


• Probability of targets is also an important factor

A1 covers R2, A2 covers R1 A1 covers R1, A2 covers R2



24

Outline








25

Assigning Agents to Targets

• Closest targets in direction of tile x with minimum Dist(x) now assigned to that agent

• May not be considered by any other agent this move

R2 assigned to A1 R2 cannot be considered by A2

• Agent now committed to those targets

• That agent will not be used by other agents to compute their Dist(x)



26

Committing Agents to Targets

A1 committed to R2 and will not move to R1

Cannot be used by A2 to determine global expected distance to R1

• Some agents may not be closest to any targets

• Agents “subsumed” by other agents– Initially, no move chosen– Are reconsidered after other agents choose directions



27

Subsumed Agents

A1 closer to both A2 closest

to neither

• Targets agents moving away from are released to subsumed agents

– ti Tj , ti Tjx where Dist(x) is minimum

– A1 chooses to move towards R2

– R1 released for consideration by other agents

– A2 now uses R1 to move left



28

Subsumed Agents



29

Overall Algorithm Structurefor each move {

while (unassigned targets && uncommitted agents) {

– find closest uncommitted agent to each unassigned target (agents with no targets are subsumed)

– for (each non-subsumed agent A) {

– A computes Dist(x) based only on other uncommitted agents

– A committed to move in direction with minimum Dist(x);

– A’s targets in that direction assigned to A;

– Targets not in that direction released for next cycle of loop

}

}

}



30

Subsumed Agents

• Agents may still be subsumed if all targets assigned to other agents– Loop ends without all agents being

assigned targets

– A1 best move is down

– Both R1 and R2 closer in that direction

– Both R1 and R2 assigned to A1

– No remaining targets for A2



31

Subsumed Agents

• Base subsumed agent move on all targets regardless of what other agents are doing

– Use original single-agent probabilistic smart terrain formula

– Gives agent appearance of doing something



32

Subsumed Agents

• Agents may eventually not be subsumed

– Agent moves to area with multiple targets

– Will move towards one target and away from others

– Those other targets now available to subsumed agents in area



33

Outline








34

Performance on Initial Example

• Player may be in one of 7 rooms, 3 with “treasure”

• 3 guards searching for player

• Probability player in a given “treasure” room = 0.2

• Probability player in a “non-treasure” room = 0.1



35

Dynamic Targets

• “Target” tiles placed one step inside each room– Gives guards appearance of “looking” in a room

• Probabilities change when guard reaches tile– Player not in room probability set to 0– Guard now influenced by other rooms



36

Performance on Initial Example



37

Initial Example Modified

• “Gold” room moved to upper left

• Guard 2 moves to jewel room instead

• Guard 1 path also altered as result



38

Ongoing Work

• Testing with actual players– Implement algorithm as game (Unreal engine)

– Goal: steal treasure while avoiding guards

– Player can see guard movement, guards use algorithm to search for player

• Do NPC guard actions appear plausible to players?


Dr. John R. Sullins

Youngstown State University



40

Player Found in Large Example

• Player tile probability set to 1

• Other target probabilities set to 0

• All guards will now converge on player

Multiagent Probabilistic Smart Terrain Dr. John R. Sullins Youngstown State University.

Documents

Transcript of Multiagent Probabilistic Smart Terrain Dr. John R. Sullins Youngstown State University.