mechanismsaggregation and segregationarpwhite/courses/5002/lectures/ant-clusterin… · the...
TRANSCRIPT
Aggregation and SegregationMechanisms
AM, EE141, Swarm Intelligence, W4-1
Outline
• Social insects (ants)• Algorithms (data clustering)• Robotics experiments
Ants
It defines a class of mechanisms exploited by social insects to coordinate andcontrol their activity via indirect interactions.
• Stigmergic mechanisms can be classified in two different categories:quantitative (or continuous) stigmergy and qualitative (or discrete)stigmergy
Stimulus
Answer
S1
R1
S2
R2
S3
R3
time
S 4
R4
S 5
R5
Stop
Definition
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)
Stigmergy
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 aprobability which increases with the degree of isolation of thecorpse
• When an ant is carrying a corpse, it will drop it with a probabilitywhich increases with the number of corpses in the vicinity
• Modulation of pick up/drop probabilities as a function of thepheromone clouds around the cluster -> quantitative (continuous)stigmergy
The probability that an agent which is not carrying an item will pickup an item
Ppick up =K+
K+ + f
Probability that an agent carrying an item will drop the item
Pdrop =f
K- + f
f : fraction of neighborhood sites occupied by itemsK-, K+: threshold constants
Algorithm for individual behavior
A Model of Corpse Clustering
( )2
)2(
t = 15
t = 0
Short term memoryat t = 15
Probability of picking up an object:
Probability of dropping an objectwhich is being carried:
fi : fraction of neighboring sitesoccupied by objects of the same typeof the object i
K+, K- : constants
Pipick up = ( K+ / ( K+ + fi ) ) 2
Pidrop = ( fi / ( K- + fi ) ) 2
Individual behavioral algorithm
Model of HarvestSorting in Ants
Aggregation andSegregation 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!
Back to slides …
Algorithms
• We define a « distance » d (or a dissimilarity) between objects in theattribute space of the object.
• For instance, in the sorting problem previously mentioned, 2 objects oiand oj can be similar or different (binary dissimilarity):
If oi and oj are identical objects then: d(oi, oj) = 0If oi and oj are different objects then: d(oi, oj) = 1
• The problem (and the algorithm) can be extended to more compleobjects described by a finite number n of attributes, each attributerepresented by a real value for instance.
• These objects can be described as points in the Rn space and d(oi, oj) asthe eucledian distance between them.
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 intra-clusters are smaller than distances inter-cluster
• We finally discretize the projected space (it can be seen as a sub-space of Z2), sothat many clusterizing agents can move around and operate on this space
Algorithm of Lumer et Faieta (1994)
Application of Clustering Algorithms to the
Classification of Objects
The agents can locally perceive a certain number of cells around their position (areas2 around the current site r of the agent)
S
S
r
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 oi, on this site f(oi) measures the meansimilarity of the object oi with the other objects oj which are in its neighborhood(within perception area sxs)
αααα : algorithm parameter which defines the dissimilarity scale
Algorithm of Lumer et Faieta (1994)
f(oi) = , if f > 01
s2[1– ]Σ
Oj ∈ Neigh(sxs) (r)
f(oi) = 0 , otherwise
α
d(oi, oj)
Application of Clustering Algorithms to the
Classification of Objects
• If all the cells s2 around the agent at site r have similar objects to oi, weobtain :
∀ Oj ∈ Neigh(sxs) (r), d(oi, oj) = 0 and f(oi) = 1
• If all the cells s2 around the agent at site r have objects highly differentto oi, we obtain :
∀ Oj ∈ Neigh(sxs) (r), d(oi, oj) = α and f(oi) = 0
Algorithm of Lumer et Faieta (1994)
Application of Clustering Algorithms to the
Classification of Objects
k1
k1 + f(oi)( )
2
{2f(oi), if f(oi) < k2
1, if f(oi) ≥ k2
If f(oi) = 1, oi has low probability to be picked upIf f(oi) = 0, oi has high probability to be picked up
Algorithm of Lumer et Faieta (1994)
Probability of an unloaded agent of picking up an object
Ppick up (oi) =
k1, k2 : threshold constants
Pdrop (oi) =
Probability of an loaded agent of dropping an object
Application of Clustering Algorithms to the
Classification of Objects
Example of collective sorting
Attribute space: 4 gaussian distributions of real numbers
20.0
15.0
10.0
5.0
0.0
-5.0
-10.0-10.0 0.0 10.0 20.0
20.0
15.0
10.0
5.0
0.0
-5.0
-10.0-10.0 0.0 10.0 20.0
Application of Clustering Algorithms to the
Classification of Objects
Points are randomly scattered on a grid of 52 X 52and clustering is performedwith 40 agents
t = 0 t = 500000
Example of collective sorting
Heuristic needed for better performances: heterogeneous agents (different speeds)and short term memory -> then 4 clusters …
Application of Clustering Algorithms to the
Classification of Objects
Robots
The mission:From local actions to global tasks: stigmergy and collectiverobotics.
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 largerclusters.
Puck Clustering (Beckers, Holland,and Deneubourg, 1994)
Puck Clustering (Beckers, Holland,and Deneubourg, 1994)
The behavior:
Puck Clustering (Beckers, Holland,and Deneubourg, 1994)
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
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 highstochastic component
• more quantitative analysis in the next lecture!
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
Puck Clustering (Beckers, Holland,and Deneubourg, 1994)
Conclusion
• Robots can form clusters using a simpler algorithm than that proposed byDeneubourg: deterministic (but stochasticity in the interactions), strictly localsensing without memory (but memory = a little bit less local … ).
• Robots can show many of the advantageous features of ant behavior (robustnessto individual failure, robustness to environmental disturbance and interferences).
• The robot system is tightly coupled to the physics of the environment, andresponds coherently.
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 forrepresenting in a land-robotic form ... but they build with particles of grit thesame 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 theratio of the area of a Leptothorax nest to a single ant.
• Qualitative/feasibility rather than quantitative/efficiency study
The Robots
• 23 cm in diameter
• 3h battery autonomy
• Motorola 68332, 16 Mb RAM
• 4 continuous emitting IRproximity 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 colordetection of the carried frisbee
Frisbee Gathering and Sorting(Holland and Melhuish, 1998)
Experimental set-up
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!
Frisbee Gathering and Sorting(Holland and Melhuish, 1998)
Frisbee Gathering (Holland andMelhuish, 1998)
Exp. 1: Results for basic clustering (10 robots, 44 frisbees)
8h 25 min, endcriterium:90% offrisbees gathered(40)
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)
• …
Frisbee Gathering (Holland andMelhuish, 1998)
Exp. 2: Could we form clusters at the edges of the arena?
"It must be emphasized that a very large arena was necessary inDeneubourg et al's experiments to obtain "bulk" clusters: in effect,ants are attracted towards the edges of the experimental arena if theseare too close to the nest, resulting in clusters almost exclusively alongthe edges."Eric Bonabeau, 1998
Test:• Vary the algorithm ok• Vary the sensors ok• Vary the arena size?
Frisbee Gathering (Holland andMelhuish, 1998)
Frisbee Gathering (Holland andMelhuish, 1998)
Exp. 2: Boundary clustering, algorithm
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
Algorithm modified:
Rule 1 probabilistic!
Frisbee Gathering (Holland andMelhuish, 1998)
Exp. 2: Boundary clustering, parameter bifurcationprobabilityof 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
0.88 1 cluster formed at edge. 40/44 at 9hrs 5m continued to be stable up to 11hrs20min.
0.85 1 major cluster formed at edge and approx. 15 singletons around the periphery.stopped after 1110hours
0.8 1 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 formedStopped at 11 hrs
0.0 All pucks taken to periphery (frame 3 0hr15m) but no single cluster formed.Stopped at 3hrs.
Frisbee Gathering (Holland andMelhuish, 1998)
Exp. 2: Boundary clustering, parameter bifurcation
p = 0.0p = 0.5p = 0.8
p = 0.88p = 0.9p = 1.0
Frisbee Gathering (Holland andMelhuish, 1998)
Exp. 2: Boundary clustering, sensory modification
Drop puck/Leave puck
Drop puck/Leave puck
wall
Mean 100.3 0
Pick up/ Retain puck
Obstacle detection only with central sensor (instead of the 3 frontal sensors)!
p =100.3/180 = 0.56
But robot movementsnot really uniformlydistributed(trajectories, no wallfollowing ) …
Frisbee Gathering (Holland andMelhuish, 1998)
Exp. 2: Boundary clustering, sensory modification
Similar to p = 0.88 in the algorithmic version!
Frisbee Sorting (Holland andMelhuish, 1998)
Exp. 3: The pull back algorithm
Rule 1:if (gripper pressed & Object ahead) then make random turn away from object 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
• Initial idea: change the compacity (pull back distance is a sensitive parameter) forspeeding up aggregation process
• Robot behavior different with ring or plain frisbees
Frisbee Sorting (Holland andMelhuish, 1998)
Exp. 3: The pull back algorithm, results (pullback distance 2.6frisbees, 6 robots)
t = 0h00 t = 1h45 t = 8h05
Annular sorting like in Leptothorax ants!
Frisbee Sorting (Holland andMelhuish, 1998)
Exp. 3: The pull back algorithm, results (pullback distance 2.6frisbees, 6 robots, end criterium: first cluster of 20 frisbees)
Trial 1 2 3 4 5
Time in hours 7.58 2.75 25.3 11.7 4.50
Number ofplains
11 12 11 10 12
High std dev
Low std dev
Frisbee Gathering and Sorting(Holland and Melhuish, 1998)
Conclusion
• Robots can form clusters using a simpler algorithm than that proposed byDeneubourg: deterministic (but stochasticity in the interactions), strictly localsensing without memory (but memory = a little bit less local … ).
• Robots can show many of the advantageous features of ant behavior (robustnessto individual failure, robustness to environmental disturbance and interferences).
• The robot system is tightly coupled to the physics of the environment, andresponds coherently.
But how about qualitative considerations? How can we improve the systemefficiency, how can we reduce the variability of the team performance, what arethe key parameters of the experiment?
Next lecture an answer attempt …