Introduction Microscopic Model Macroscopic Model Conclusion Bridge Experiment with Overcrowding Swarm Intelligence Course Project S´ ebastien Cuendet & Jean-Philippe Pellet { sebastien.cuendet, jean-philippe.pellet } @epfl.ch 9th February, 2006
Introduction Microscopic Model Macroscopic Model Conclusion Outline Introduction 1 Microscopic Model 2 Macroscopic Model 3 Conclusion 4
Introduction Microscopic Model Macroscopic Model Conclusion Outline Introduction 1 Microscopic Model 2 Macroscopic Model 3 Conclusion 4
Introduction Microscopic Model Macroscopic Model Conclusion Asymmetric Bridge Experiment Given number of agents/ants must bring back a maximal amount of food Two paths: short path (length l ), long path (length r · l ) Add obstacle avoidance Study effect of pheromone F (Food source) S L N (Nest)
Introduction Microscopic Model Macroscopic Model Conclusion Outline Introduction 1 Microscopic Model 2 Macroscopic Model 3 Conclusion 4
Introduction Microscopic Model Macroscopic Model Conclusion Model Description Microscopic model: PFSM Fixed probabilities and dynamic probabilities Dynamic probs depend on system’s past history ⇒ Not a markovian model Modeled aspects: Path length Collisions Pheromone
Introduction Microscopic Model Macroscopic Model Conclusion Model Description Microscopic model: PFSM Fixed probabilities and dynamic probabilities Dynamic probs depend on system’s past history ⇒ Not a markovian model Modeled aspects: Path length Collisions Pheromone
Introduction Microscopic Model Macroscopic Model Conclusion Designing the Model: Iteration I F p FS p FL 1/(2 T L ) 1/(2 T S ) S L 1/(2 T S ) 1/(2 T L ) p NS p NL N Simplest case, no collision No pheromones:, p NS = p NL = p N / 2, p FS = p FL = 1 / 2 Path length: modeled with outgoing prob ( T L = r · T S ) Implicit U-turn possibility
Introduction Microscopic Model Macroscopic Model Conclusion Designing the Model: Iteration II F p FS p FL 1/(2 T L ) 1/(2 T S ) p SA p LA A L A S S L 1/(2 T S ) 1/(2 T L ) 1/ T A 1/ T A p NS p NL N Added collision prob (dynamic): p SA ( k ) = p r · ( S ( k ) − 1), p LA ( k ) = p r r · ( L ( k ) − 1) Come back from avoidance probabilistically with prob 1 / T A p r , T A : new model parameters. Still implicit U-turn possibility
Introduction Microscopic Model Macroscopic Model Conclusion Designing the Model: Iteration III F p FS p FL 1/ T S 1/ T L p SA p SA p LA p LA A S2 S 2 S 1 A S1 A L1 L 1 L 2 A L2 1/ T A 1/ T A 1/ T A 1/ T A p NS p NL 1/ T L 1/ T S N Duplicated some states: now way up and way down; no U-turn ⇒ Probabilities must be adapted Collision: p AS 1 ( k ) = p AS 2 ( k ) = p r · ( S 1 ( k ) + S 2 ( k ) − 1) p AL 1 ( k ) = p AL 2 ( k ) = p r r · ( L 1 ( k ) + L 2 ( k ) − 1) How to implement pheromones?
Introduction Microscopic Model Macroscopic Model Conclusion Modeling Pheromones I Idea I: count number of agents in states S 1 and S 2 , use as estimate for pheromone deposited on S . ⇒ Problem: doesn’t work (e.g. longer path is marked more). Pheromone should mark most successful path and take into account how fast ants get back using this path Idea II: Use two types of pheromones: one deposited on the way up and “smelled” on the way down; one deposited on the way down and smelled on the way up ⇒ Problem: still not OK (e.g. ants that have just entered the long path have the same influence as ants about to leave the short path) Idea III: use special exit states at the end of the paths; count ants going through them ⇒ It works!
Introduction Microscopic Model Macroscopic Model Conclusion Modeling Pheromones I Idea I: count number of agents in states S 1 and S 2 , use as estimate for pheromone deposited on S . ⇒ Problem: doesn’t work (e.g. longer path is marked more). Pheromone should mark most successful path and take into account how fast ants get back using this path Idea II: Use two types of pheromones: one deposited on the way up and “smelled” on the way down; one deposited on the way down and smelled on the way up ⇒ Problem: still not OK (e.g. ants that have just entered the long path have the same influence as ants about to leave the short path) Idea III: use special exit states at the end of the paths; count ants going through them ⇒ It works!
Introduction Microscopic Model Macroscopic Model Conclusion Modeling Pheromones I Idea I: count number of agents in states S 1 and S 2 , use as estimate for pheromone deposited on S . ⇒ Problem: doesn’t work (e.g. longer path is marked more). Pheromone should mark most successful path and take into account how fast ants get back using this path Idea II: Use two types of pheromones: one deposited on the way up and “smelled” on the way down; one deposited on the way down and smelled on the way up ⇒ Problem: still not OK (e.g. ants that have just entered the long path have the same influence as ants about to leave the short path) Idea III: use special exit states at the end of the paths; count ants going through them ⇒ It works!
Introduction Microscopic Model Macroscopic Model Conclusion Designing the Model: Iteration III (again) F p FS p FL 1/ T S 1/ T L p SA p SA p LA p LA S 1 A S1 A L1 A S2 S 2 L 1 L 2 A L2 1/ T A 1/ T A 1/ T A 1/ T A p NS p NL 1/ T L 1/ T S N (what we had previously)
Introduction Microscopic Model Macroscopic Model Conclusion Designing the Model: Iteration IV F p FS 1 1 p FL ^ ^ S 1 L 1 1/ T S 1/ T L p SA p SA p LA p LA S 2 S 1 A S1 A L1 L 1 L 2 A L2 A S2 1/ T A 1/ T A 1/ T A 1/ T A 1/ T S 1/ T L p NS p NL ^ ^ S 2 L 2 1 1 N Added exit states � S 1 , � S 2 , � L 1 , � L 2 Ants remain only one time step in exit states Neglect collision prob in exit states Pheromones implemented by varying p FS , p FL , p NS and p NL
Introduction Microscopic Model Macroscopic Model Conclusion Modeling Pheromones II No pheromone: p NS = p NL = p N / 2 p FS = p FL = 1 / 2 With pheromone: “Smelled” pheromone for S at time k from the nest: j max j max � � h j · � h j · � Φ NS ( k ) = S 2 ( k − j ) , Φ NL ( k ) = L 2 ( k − j ) j =0 j =0 Transition prob: [ q + Φ NS ( k )] n p NS ( k ) = p N · [ q + Φ NS ( k )] n + [ q + Φ NL ( k )] n New parameters: p N , h , n , q , ( j max )
Introduction Microscopic Model Macroscopic Model Conclusion Modeling Pheromones II No pheromone: p NS = p NL = p N / 2 p FS = p FL = 1 / 2 With pheromone: “Smelled” pheromone for S at time k from the nest: j max j max � � h j · � h j · � Φ NS ( k ) = S 2 ( k − j ) , Φ NL ( k ) = L 2 ( k − j ) j =0 j =0 Transition prob: [ q + Φ NS ( k )] n p NS ( k ) = p N · [ q + Φ NS ( k )] n + [ q + Φ NL ( k )] n New parameters: p N , h , n , q , ( j max )
Introduction Microscopic Model Macroscopic Model Conclusion Modeling Pheromones II No pheromone: p NS = p NL = p N / 2 p FS = p FL = 1 / 2 With pheromone: “Smelled” pheromone for S at time k from the nest: j max j max � � h j · � h j · � Φ NS ( k ) = S 2 ( k − j ) , Φ NL ( k ) = L 2 ( k − j ) j =0 j =0 Transition prob: [ q + Φ NS ( k )] n p NS ( k ) = p N · [ q + Φ NS ( k )] n + [ q + Φ NL ( k )] n New parameters: p N , h , n , q , ( j max )
Introduction Microscopic Model Macroscopic Model Conclusion Outline Introduction 1 Microscopic Model 2 Macroscopic Model 3 Conclusion 4
Introduction Microscopic Model Macroscopic Model Conclusion Macroscopic Model Equations: just read the PFSM, set of non-linear difference equations of the form S 1 ( k +1) = S 1 ( k )+ p NS · N ( k )+ p A · A S 1 ( k ) − p S · S 1 ( k ) − p SA · S 1 ( k ) Goal: determine optimal evaporation rate h given ratio r . Macroscopic equation are difficult to solve ⇒ Determine optimal h with macrosimulation
Introduction Microscopic Model Macroscopic Model Conclusion Outline Introduction 1 Microscopic Model 2 Macroscopic Model 3 Conclusion 4
Introduction Microscopic Model Macroscopic Model Conclusion Conclusion & Outlook Model works according to previous case studies of the trail laying/following mechanism Optimal evaporation rate h is monotonic function of the ratio r , also when taking into account the overcrowding effet Further work could include: Modeling of more aspects (geometry of the paths and of the robots, U-turn prob, wall avoidance, etc.) Realistic simulation or real-robot implementation to try to reach a zero-free parameter model
Introduction Microscopic Model Macroscopic Model Conclusion Conclusion & Outlook Model works according to previous case studies of the trail laying/following mechanism Optimal evaporation rate h is monotonic function of the ratio r , also when taking into account the overcrowding effet Further work could include: Modeling of more aspects (geometry of the paths and of the robots, U-turn prob, wall avoidance, etc.) Realistic simulation or real-robot implementation to try to reach a zero-free parameter model
Introduction Microscopic Model Macroscopic Model Conclusion Thanks for your attention!
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