Aggregation and Segregation Mechanisms. AM, EE141, Swarm Intelligence, W4-1

Transcription

1 Aggregation and Segregation Mechanisms AM, EE141, Swarm Intelligence, W4-1

2 Outline Social insects (ants) Algorithms (data clustering) Robotics experiments

3 Ants

4 Stigmergy Definition It defines a class of mechanisms exploited by social insects to coordinate and control their activity via indirect interactions. Answer R 1 R 2 R 3 R 4 R 5 Stimulus S 1 S 2 S 3 S 4 S 5 Stop time Stigmergic mechanisms can be classified in two different categories: quantitative (or continuous) stigmergy and qualitative (or discrete) stigmergy

5 Stigmergy Example of qualitative stigmergy Example of quantitative stigmergy More detail in Week 6! Duration of aggregation process: 48 h! Reduction of the spread of infection? Chretien (1996)

6 A Model of Corpse Clustering Characteristics of the algorithm for individual behavior (Deneubourg et al., 1991) When an ant encounters a corpse, it will pick it up with a probability which increases with the degree of isolation of the corpse When an ant is carrying a corpse, it will drop it with a probability which increases with the number of corpses in the vicinity Modulation of pick up/drop probabilities as a function of the pheromone clouds around the cluster -> quantitative (continuous) stigmergy

7 A Model of Corpse Clustering Algorithm for individual behavior The probability that an agent which is not carrying an item will pick up an item P pick up = ( K + K + + f ) 2 Probability that an agent carrying an item will drop the item P drop = ( ) 2 f K - + f f : fraction of neighborhood sites occupied by items K -, K + : threshold constants

8 Model of Harvest Sorting in Ants Individual behavioral algorithm Probability of picking up an object: t = 0 P i pick up = ( K+ / ( K + + f i ) ) 2 t = 15 Probability of dropping an object which is being carried: P i drop = ( f i / ( K- + f i ) ) 2 f i : fraction of neighboring sites occupied by objects of the same type of the object i K +, K - : constants Short term memory at t = 15

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10 Aggregation and Segregation Models Explanation of cemetery organization in Lasius niger, Pheidole pallidula, and Messor Sancta ant species ok Explanation of brood sorting in Leptothorax ants (concentric annular sorting) unexplained!

11 Back to slides

12 Algorithms

13 Application of Clustering Algorithms to the Classification of Objects We define a «distance» d (or a dissimilarity) between objects in the attribute space of the object. For instance, in the sorting problem previously mentioned, 2 objects o i and o j can be similar or different (binary dissimilarity): If o i and o j are identical objects then: d(o i, o j ) = 0 If o i and o j are different objects then: d(o i, o j ) = 1 The problem (and the algorithm) can be extended to more comple objects described by a finite number n of attributes, each attribute represented by a real value for instance. These objects can be described as points in the R n space and d(o i, o j ) as the eucledian distance between them.

14 Algorithm of Lumer et Faieta (1994) Application of Clustering Algorithms to the Classification of Objects The attribute space is projected on a smaller dimension space (e.g. l=2) Assumption: the projection space has to be chosen so that the distances intraclusters are smaller than distances inter-cluster We finally discretize the projected space (it can be seen as a sub-space of Z 2 ), so that many clusterizing agents can move around and operate on this space

15 Application of Clustering Algorithms to the Classification of Objects Algorithm of Lumer et Faieta (1994) The agents can locally perceive a certain number of cells around their position (area s 2 around the current site r of the agent) r S S

16 Algorithm of Lumer et Faieta (1994) Application of Clustering Algorithms to the Classification of Objects At time t, an agent at the site r finds an object o i, on this site f(o i ) measures the mean similarity of the object o i with the other objects o j which are in its neighborhood (within perception area sxs) 1 d(o f(o i ) = Σ i, o j )] [1, if f > 0 s 2 α O j Neigh (sxs) (r) f(o i ) = 0, otherwise α : algorithm parameter which defines the dissimilarity scale

17 Algorithm of Lumer et Faieta (1994) If all the cells s 2 around the agent at site r have similar objects to o i, we obtain : O j Neigh (sxs) (r), d(o i, o j ) = 0 and f(o i ) = 1 Application of Clustering Algorithms to the Classification of Objects If all the cells s 2 around the agent at site r have objects highly different to o i, we obtain : O j Neigh (sxs) (r), d(o i, o j ) = α and f(o i ) = 0

18 Algorithm of Lumer et Faieta (1994) Probability of an unloaded agent of picking up an object Application of Clustering Algorithms to the Classification of Objects P pick up (o i ) = ( k 1 ) 2 k 1 + f(o i ) If f(o i ) = 1, o i has low probability to be picked up If f(o i ) = 0, o i has high probability to be picked up Probability of an loaded agent of dropping an object P drop (o i ) = { 2f(o i ), if f(o i ) < k 2 1, if f(o i ) k 2 k 1, k 2 : threshold constants

19 Example of collective sorting 20.0 Application of Clustering Algorithms to the Classification of Objects Attribute space: 4 gaussian distributions of real numbers

20 Example of collective sorting Application of Clustering Algorithms to the Classification of Objects Points are randomly scattered on a grid of 52 X 52and clustering is performed with 40 agents t = 0 t = Heuristic needed for better performances: heterogeneous agents (different speeds) and short term memory -> then 4 clusters

21 Robots

22 Puck Clustering (Beckers, Holland, and Deneubourg, 1994) The mission: From local actions to global tasks: stigmergy and collective robotics. The plan: Give the robot some means of moving some discrete items. Give it a start by enabling it to make small clusters. Think of some way of estimating local density so that it can use the Deneubourg algorithm to make progressively larger clusters.

23 Puck Clustering (Beckers, Holland, and Deneubourg, 1994)

24 The behavior: Puck Clustering (Beckers, Holland, and Deneubourg, 1994)

25 Puck Clustering (Beckers, Holland, and Deneubourg, 1994) How does it works? probability of leaving a puck on a cluster increases with the size of the cluster probability of taking a puck from a cluster decreases with the size of the cluster so rate of growth increases with size adding a puck to a cluster increases its size taking a puck from a cluster reduces its size so the feedback is always positive The sum of the rates of growth over all clusters will be zero (conservation of pucks) Therefore the rate of growth of at least the smallest cluster must be negative So a group of n clusters will tend to become (n-1) clusters...and so on

26 Puck Clustering (Beckers, Holland, and Deneubourg, 1994) Why a single cluster? clusters of 2 or less pucks are irreversibly eliminated noise influence play a major role: algorithm is deterministic but interactions robot-to-robot and robot-to-environment have a high stochastic component more quantitative analysis in the next lecture!

27 Puck Clustering (Beckers, Holland, and Deneubourg, 1994) Other features of the robot system sensitive to friction and irregularities on floor will form cluster around a suitable seed robots are all different (small heterogeneities of the components) robots change with time (battery life, general aging) grippers entangling (mechanical interferences) proximity sensors interferences (continuous emission) puck lost by turning on the spot

28 Puck Clustering (Beckers, Holland, and Deneubourg, 1994) Conclusion Robots can form clusters using a simpler algorithm than that proposed by Deneubourg: deterministic (but stochasticity in the interactions), strictly local sensing without memory (but memory = a little bit less local ). Robots can show many of the advantageous features of ant behavior (robustness to individual failure, robustness to environmental disturbance and interferences). The robot system is tightly coupled to the physics of the environment, and responds coherently.

29 Frisbee Gathering and Sorting (Holland and Melhuish, 1998) Bio-mimicking experiment: Leptothorax ants Live in cracks in rocks Sort their brood Perform nest migrations: - find a new nest site - move the queen and brood there - build a surrounding wall - sort the brood Because of the 2D habitat and the interesting behaviors, ideal subjects for representing in a land-robotic form... but they build with particles of grit the same width as their bodies ( blind bulldozing )... so we need building materials the same width as the robots Frisbees Arena s area is 1760 times the area of a robot: same order of magnitude as the ratio of the area of a Leptothorax nest to a single ant. Qualitative/feasibility rather than quantitative/efficiency study

30 Frisbee Gathering and Sorting (Holland and Melhuish, 1998) The Robots 23 cm in diameter 3h battery autonomy Motorola 68332, 16 Mb RAM 4 continuous emitting IR proximity sensors Microswitch on the gripper (threshold between 1 and 2 fresbees), locking-unlocking frisbee operations controlled by an actuator Double optical sensor (color detection) for center and periphery color detection of the carried frisbee

31 Experimental set-up Frisbee Gathering and Sorting (Holland and Melhuish, 1998)

32 Frisbee Gathering and Sorting (Holland and Melhuish, 1998) Exp. 1: behavior for basic clustering Rule 1: if (gripper pressed & Object ahead) then make random turn away from object Rule 2: if (gripper pressed & no Object ahead) then reverse small distance make random turn left or right Rule 3: go forward Modified Beckers et al. basic behavior for rigid walls/robots!

33 Frisbee Gathering (Holland and Melhuish, 1998) Exp. 1: Results for basic clustering (10 robots, 44 frisbees) 8h 25 min, end criterium: 90% of frisbees gathered (40)

34 Frisbee Gathering (Holland and Melhuish, 1998) Exp. 1: comparison with performance Beckers et al. 94 Beckers et al. 1994: 81 pucks and 3 robots in 1h 45 min Holland et al. 1998: 40 frisbees and 10 robots in 8h 25 min Why? No quantitative comparison, modelling up to date Different arena s area, different robot speed Cluster of 1 object (Holland 98) vs. cluster of 2 objects (Beckers 94) irreversibly removed Noise in cluster shape (compacity of the clusters)

35 Frisbee Gathering (Holland and Melhuish, 1998) Exp. 2: Could we form clusters at the edges of the arena? "It must be emphasized that a very large arena was necessary in Deneubourg et al's experiments to obtain "bulk" clusters: in effect, ants are attracted towards the edges of the experimental arena if these are too close to the nest, resulting in clusters almost exclusively along the edges." Eric Bonabeau, 1998 Test: Vary the algorithm ok Vary the sensors ok Vary the arena size?

36 Frisbee Gathering (Holland and Melhuish, 1998) Exp. 2: Boundary clustering, algorithm Algorithm modified: Rule 1 probabilistic! Rule 1: if (gripper pressed & Object ahead) then with probability p make random turn away from object else with probability (1-p) reverse small distance (dropping the frisbee) make random turn left or right Rule 2: if (gripper pressed & no Object ahead) then reverse small distance (dropping the frisbee) make random turn left or right Rule 3: go forward

37 Exp. 2: Boundary clustering, parameter bifurcation Frisbee Gathering (Holland and Melhuish, 1998) probability of retention p RESULTS 1.0 leads to a central cluster after 6 hours 35 minutes 0.95 leads to a central cluster, stopped when 2 main central clusters formed. Stopped ~2.5hours 0.9 leads to a central cluster, stopped when 2 main central clusters formed. Stopped ~5hours cluster formed at edge. 40/44 at 9hrs 5m continued to be stable up to 11hrs 20min major cluster formed at edge and approx. 15 singletons around the periphery. stopped after 1110hours major cluster formed at edge and approx. 15 singletons around the periphery. Stopped after 11hrs 0.5 All pucks taken to periphery (frame 8, 0hr40mins)but no single cluster formed Stopped at 11 hrs 0.0 All pucks taken to periphery (frame 3 0hr15m) but no single cluster formed. Stopped at 3hrs.

38 Frisbee Gathering (Holland and Melhuish, 1998) Exp. 2: Boundary clustering, parameter bifurcation p = 1.0 p = 0.9 p = 0.88 p = 0.8 p = 0.5 p = 0.0

39 Exp. 2: Boundary clustering, sensory modification Frisbee Gathering (Holland and Melhuish, 1998) Obstacle detection only with central sensor (instead of the 3 frontal sensors)! wall p =100.3/180 = 0.56 Drop puck/ Leave puck Pick up/ Retain puck Mean Drop puck/ Leave puck But robot movements not really uniformly distributed (trajectories, no wall following )

40 Exp. 2: Boundary clustering, sensory modification Frisbee Gathering (Holland and Melhuish, 1998) Similar to p = 0.88 in the algorithmic version!

41 Exp. 3: The pull back algorithm Rule 1: if (gripper pressed & Object ahead) then make random turn away from object Frisbee Sorting (Holland and Melhuish, 1998) Initial idea: change the compacity (pull back distance is a sensitive parameter) for speeding up aggregation process Robot behavior different with ring or plain frisbees Rule 2: if (gripper pressed & no Object ahead) then if plain then lower pin and reverse for pull-back distance raise pin endif reverse small distance make random turn left or right

42 Frisbee Sorting (Holland and Melhuish, 1998) Exp. 3: The pull back algorithm, results (pullback distance 2.6 frisbees, 6 robots) t = 0h00 t = 1h45 t = 8h05 Annular sorting like in Leptothorax ants!

43 Frisbee Sorting (Holland and Melhuish, 1998) Exp. 3: The pull back algorithm, results (pullback distance 2.6 frisbees, 6 robots, end criterium: first cluster of 20 frisbees) Trial Time in hours High std dev Number of plains Low std dev

44 Frisbee Gathering and Sorting (Holland and Melhuish, 1998) Conclusion Robots can form clusters using a simpler algorithm than that proposed by Deneubourg: deterministic (but stochasticity in the interactions), strictly local sensing without memory (but memory = a little bit less local ). Robots can show many of the advantageous features of ant behavior (robustness to individual failure, robustness to environmental disturbance and interferences). The robot system is tightly coupled to the physics of the environment, and responds coherently. But how about qualitative considerations? How can we improve the system efficiency, how can we reduce the variability of the team performance, what are the key parameters of the experiment? Next lecture an answer attempt